diff --git a/hist/histv7/CMakeLists.txt b/hist/histv7/CMakeLists.txt
index e69de29bb2d1d..4e5918d833f87 100644
--- a/hist/histv7/CMakeLists.txt
+++ b/hist/histv7/CMakeLists.txt
@@ -0,0 +1,11 @@
+ROOT_STANDARD_LIBRARY_PACKAGE(ROOTHist
+  HEADERS
+    ROOT/RLinearizedIndex.hxx
+    ROOT/RRegularAxis.hxx
+    ROOT/RVariableBinAxis.hxx
+  NO_SOURCES
+  DEPENDENCIES
+    Core
+)
+
+ROOT_ADD_TEST_SUBDIRECTORY(test)
diff --git a/hist/histv7/doc/DesignImplementation.md b/hist/histv7/doc/DesignImplementation.md
index 4c6acec92e668..7ccbffb7aaa06 100644
--- a/hist/histv7/doc/DesignImplementation.md
+++ b/hist/histv7/doc/DesignImplementation.md
@@ -71,3 +71,6 @@ The implementation uses standard [C++17](https://en.cppreference.com/w/cpp/17.ht
  * No ROOT types, to make sure the histogram package can be compiled standalone.
 
 Small objects are passed by value instead of by reference (`RBinIndex`, `RWeight`).
+
+Complex objects, such as `std::vector`, that have to be copied (for example in a constructor) are also accepted by value.
+This allows a single overload that can efficiently take expiring ("moved") objects.
diff --git a/hist/histv7/inc/LinkDef.h b/hist/histv7/inc/LinkDef.h
new file mode 100644
index 0000000000000..e69de29bb2d1d
diff --git a/hist/histv7/inc/ROOT/RLinearizedIndex.hxx b/hist/histv7/inc/ROOT/RLinearizedIndex.hxx
new file mode 100644
index 0000000000000..fe10fc1d39cd6
--- /dev/null
+++ b/hist/histv7/inc/ROOT/RLinearizedIndex.hxx
@@ -0,0 +1,28 @@
+/// \warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback
+/// is welcome!
+
+#ifndef ROOT_RLinearizedIndex
+#define ROOT_RLinearizedIndex
+
+#include <cstddef>
+
+namespace ROOT {
+namespace Experimental {
+
+/**
+A linearized index that can be invalid.
+
+For example, when an argument is outside the axis and underflow / overflow bins are disabled.
+
+\warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback is
+welcome!
+*/
+struct RLinearizedIndex final {
+   std::size_t fIndex;
+   bool fValid;
+};
+
+} // namespace Experimental
+} // namespace ROOT
+
+#endif
diff --git a/hist/histv7/inc/ROOT/RRegularAxis.hxx b/hist/histv7/inc/ROOT/RRegularAxis.hxx
new file mode 100644
index 0000000000000..128b0649469c6
--- /dev/null
+++ b/hist/histv7/inc/ROOT/RRegularAxis.hxx
@@ -0,0 +1,93 @@
+/// \warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback
+/// is welcome!
+
+#ifndef ROOT_RRegularAxis
+#define ROOT_RRegularAxis
+
+#include "RLinearizedIndex.hxx"
+
+#include <cstddef>
+
+namespace ROOT {
+namespace Experimental {
+
+/**
+A regular axis with equidistant bins in the interval \f$[fLow, fHigh)\f$.
+
+For example, the following creates a regular axis with 10 normal bins between 5 and 15:
+~~~ {.cxx}
+ROOT::Experimental::RRegularAxis axis(10, 5, 15);
+~~~
+
+It is possible to disable underflow and overflow bins by passing `enableFlowBins = false`. In that case, arguments
+outside the axis will be silently discarded.
+
+\warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback is
+welcome!
+*/
+class RRegularAxis final {
+   /// The number of normal bins
+   std::size_t fNumNormalBins;
+   /// The lower end of the axis interval
+   double fLow;
+   /// The upper end of the axis interval
+   double fHigh;
+   /// The cached inverse of the bin width to speed up ComputeLinearizedIndex
+   double fInvBinWidth; //!
+   /// Whether underflow and overflow bins are enabled
+   bool fEnableFlowBins;
+
+public:
+   /// Construct a regular axis object.
+   ///
+   /// \param[in] numNormalBins the number of normal bins
+   /// \param[in] low the lower end of the axis interval (inclusive)
+   /// \param[in] high the upper end of the axis interval (exclusive)
+   /// \param[in] enableFlowBins whether to enable underflow and overflow bins
+   RRegularAxis(std::size_t numNormalBins, double low, double high, bool enableFlowBins = true)
+      : fNumNormalBins(numNormalBins), fLow(low), fHigh(high), fEnableFlowBins(enableFlowBins)
+   {
+      // FIXME: should validate numNormalBins > 0 and low < high
+      fInvBinWidth = numNormalBins / (high - low);
+   }
+
+   std::size_t GetNumNormalBins() const { return fNumNormalBins; }
+   std::size_t GetTotalNumBins() const { return fEnableFlowBins ? fNumNormalBins + 2 : fNumNormalBins; }
+   double GetLow() const { return fLow; }
+   double GetHigh() const { return fHigh; }
+   bool HasFlowBins() const { return fEnableFlowBins; }
+
+   friend bool operator==(const RRegularAxis &lhs, const RRegularAxis &rhs)
+   {
+      return lhs.fNumNormalBins == rhs.fNumNormalBins && lhs.fLow == rhs.fLow && lhs.fHigh == rhs.fHigh &&
+             lhs.fEnableFlowBins == rhs.fEnableFlowBins;
+   }
+
+   /// Compute the linarized index for a single argument.
+   ///
+   /// The normal bins have indices \f$0\f$ to \f$fNumNormalBins - 1\f$, the underflow bin has index
+   /// \f$fNumNormalBins\f$, and the overflow bin has index \f$fNumNormalBins + 1\f$. If the argument is outside the
+   /// interval \f$[fLow, fHigh)\f$ and the flow bins are disabled, the return value is invalid.
+   ///
+   /// \param[in] x the argument
+   /// \return the linearized index that may be invalid
+   RLinearizedIndex ComputeLinearizedIndex(double x) const
+   {
+      bool underflow = x < fLow;
+      // Put NaNs into overflow bin.
+      bool overflow = !(x < fHigh);
+      if (underflow) {
+         return {fNumNormalBins, fEnableFlowBins};
+      } else if (overflow) {
+         return {fNumNormalBins + 1, fEnableFlowBins};
+      }
+
+      std::size_t bin = (x - fLow) * fInvBinWidth;
+      return {bin, true};
+   }
+};
+
+} // namespace Experimental
+} // namespace ROOT
+
+#endif
diff --git a/hist/histv7/inc/ROOT/RVariableBinAxis.hxx b/hist/histv7/inc/ROOT/RVariableBinAxis.hxx
new file mode 100644
index 0000000000000..0858f9f7dca82
--- /dev/null
+++ b/hist/histv7/inc/ROOT/RVariableBinAxis.hxx
@@ -0,0 +1,91 @@
+/// \warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback
+/// is welcome!
+
+#ifndef ROOT_RVariableBinAxis
+#define ROOT_RVariableBinAxis
+
+#include "RLinearizedIndex.hxx"
+
+#include <cstddef>
+#include <utility>
+#include <vector>
+
+namespace ROOT {
+namespace Experimental {
+
+/**
+An axis with variable bins defined by their edges.
+
+For example, the following creates an axis with 3 log-spaced bins:
+~~~ {.cxx}
+std::vector<double> binEdges = {1, 10, 100, 1000};
+ROOT::Experimental::RVariableBinAxis axis(binEdges);
+~~~
+
+It is possible to disable underflow and overflow bins by passing `enableFlowBins = false`. In that case, arguments
+outside the axis will be silently discarded.
+
+\warning This is part of the ROOT 7 prototype! It will change without notice. It might trigger earthquakes. Feedback is
+welcome!
+*/
+class RVariableBinAxis final {
+   /// The (ordered) edges of the normal bins
+   std::vector<double> fBinEdges;
+   /// Whether underflow and overflow bins are enabled
+   bool fEnableFlowBins;
+
+public:
+   /// Construct an axis object with variable bins.
+   ///
+   /// \param[in] binEdges the (ordered) edges of the normal bins
+   /// \param[in] enableFlowBins whether to enable underflow and overflow bins
+   RVariableBinAxis(std::vector<double> binEdges, bool enableFlowBins = true)
+      : fBinEdges(std::move(binEdges)), fEnableFlowBins(enableFlowBins)
+   {
+      // FIXME: should validate that fBinEdges is sorted
+   }
+
+   std::size_t GetNumNormalBins() const { return fBinEdges.size() - 1; }
+   std::size_t GetTotalNumBins() const { return fEnableFlowBins ? fBinEdges.size() + 1 : fBinEdges.size() - 1; }
+   const std::vector<double> &GetBinEdges() const { return fBinEdges; }
+   bool HasFlowBins() const { return fEnableFlowBins; }
+
+   friend bool operator==(const RVariableBinAxis &lhs, const RVariableBinAxis &rhs)
+   {
+      return lhs.fBinEdges == rhs.fBinEdges && lhs.fEnableFlowBins == rhs.fEnableFlowBins;
+   }
+
+   /// Compute the linarized index for a single argument.
+   ///
+   /// The normal bins have indices \f$0\f$ to \f$fBinEdges.size() - 2\f$, the underflow bin has index
+   /// \f$fBinEdges.size() - 1\f$, and the overflow bin has index \f$fBinEdges.size()\f$. If the argument is outside all
+   /// bin edges and the flow bins are disabled, the return value is invalid.
+   ///
+   /// \param[in] x the argument
+   /// \return the linearized index that may be invalid
+   RLinearizedIndex ComputeLinearizedIndex(double x) const
+   {
+      bool underflow = x < fBinEdges.front();
+      // Put NaNs into overflow bin.
+      bool overflow = !(x < fBinEdges.back());
+      if (underflow) {
+         return {fBinEdges.size() - 1, fEnableFlowBins};
+      } else if (overflow) {
+         return {fBinEdges.size(), fEnableFlowBins};
+      }
+
+      // TODO (for later): The following can be optimized with binary search...
+      for (std::size_t bin = 0; bin < fBinEdges.size() - 2; bin++) {
+         if (x < fBinEdges[bin + 1]) {
+            return {bin, true};
+         }
+      }
+      std::size_t bin = fBinEdges.size() - 2;
+      return {bin, true};
+   }
+};
+
+} // namespace Experimental
+} // namespace ROOT
+
+#endif
diff --git a/hist/histv7/test/CMakeLists.txt b/hist/histv7/test/CMakeLists.txt
new file mode 100644
index 0000000000000..b89bb983c5127
--- /dev/null
+++ b/hist/histv7/test/CMakeLists.txt
@@ -0,0 +1,2 @@
+ROOT_ADD_GTEST(hist_regular hist_regular.cxx LIBRARIES ROOTHist)
+ROOT_ADD_GTEST(hist_variable hist_variable.cxx LIBRARIES ROOTHist)
diff --git a/hist/histv7/test/hist_regular.cxx b/hist/histv7/test/hist_regular.cxx
new file mode 100644
index 0000000000000..7c28c1816653f
--- /dev/null
+++ b/hist/histv7/test/hist_regular.cxx
@@ -0,0 +1,89 @@
+#include "hist_test.hxx"
+
+#include <limits>
+
+TEST(RRegularAxis, Constructor)
+{
+   static constexpr std::size_t Bins = 20;
+   RRegularAxis axis(Bins, 0, Bins);
+   EXPECT_EQ(axis.GetNumNormalBins(), Bins);
+   EXPECT_EQ(axis.GetTotalNumBins(), Bins + 2);
+   EXPECT_EQ(axis.GetLow(), 0);
+   EXPECT_EQ(axis.GetHigh(), Bins);
+   EXPECT_TRUE(axis.HasFlowBins());
+
+   axis = RRegularAxis(Bins, 0, Bins, /*enableFlowBins=*/false);
+   EXPECT_EQ(axis.GetNumNormalBins(), Bins);
+   EXPECT_EQ(axis.GetTotalNumBins(), Bins);
+   EXPECT_FALSE(axis.HasFlowBins());
+}
+
+TEST(RRegularAxis, Equality)
+{
+   static constexpr std::size_t Bins = 20;
+   const RRegularAxis axisA(Bins, 0, Bins);
+   const RRegularAxis axisANoFlowBins(Bins, 0, Bins, /*enableFlowBins=*/false);
+   const RRegularAxis axisA2(Bins, 0, Bins);
+   const RRegularAxis axisB(Bins / 2, 0, Bins);
+   const RRegularAxis axisC(Bins, 0, Bins / 2);
+   const RRegularAxis axisD(Bins, Bins / 2, Bins);
+
+   EXPECT_TRUE(axisA == axisA);
+   EXPECT_TRUE(axisA == axisA2);
+   EXPECT_TRUE(axisA2 == axisA);
+
+   EXPECT_FALSE(axisA == axisANoFlowBins);
+
+   EXPECT_FALSE(axisA == axisB);
+   EXPECT_FALSE(axisA == axisC);
+   EXPECT_FALSE(axisA == axisD);
+
+   EXPECT_FALSE(axisB == axisC);
+   EXPECT_FALSE(axisB == axisD);
+
+   EXPECT_FALSE(axisC == axisD);
+   EXPECT_FALSE(axisD == axisC);
+}
+
+TEST(RRegularAxis, ComputeLinearizedIndex)
+{
+   static constexpr std::size_t Bins = 20;
+   const RRegularAxis axis(Bins, 0, Bins);
+   const RRegularAxis axisNoFlowBins(Bins, 0, Bins, /*enableFlowBins=*/false);
+
+   // Underflow
+   static constexpr double NegativeInfinity = -std::numeric_limits<double>::infinity();
+   static constexpr double UnderflowLarge = -static_cast<double>(Bins);
+   static constexpr double UnderflowSmall = -0.1;
+   for (double underflow : {NegativeInfinity, UnderflowLarge, UnderflowSmall}) {
+      auto linIndex = axis.ComputeLinearizedIndex(underflow);
+      EXPECT_EQ(linIndex.fIndex, Bins);
+      EXPECT_TRUE(linIndex.fValid);
+      linIndex = axisNoFlowBins.ComputeLinearizedIndex(underflow);
+      EXPECT_EQ(linIndex.fIndex, Bins);
+      EXPECT_FALSE(linIndex.fValid);
+   }
+
+   for (std::size_t i = 0; i < Bins; i++) {
+      auto linIndex = axis.ComputeLinearizedIndex(i + 0.5);
+      EXPECT_EQ(linIndex.fIndex, i);
+      EXPECT_TRUE(linIndex.fValid);
+      linIndex = axisNoFlowBins.ComputeLinearizedIndex(i + 0.5);
+      EXPECT_EQ(linIndex.fIndex, i);
+      EXPECT_TRUE(linIndex.fValid);
+   }
+
+   // Overflow
+   static constexpr double PositiveInfinity = std::numeric_limits<double>::infinity();
+   static constexpr double NaN = std::numeric_limits<double>::quiet_NaN();
+   static constexpr double OverflowLarge = static_cast<double>(Bins * 2);
+   static constexpr double OverflowSmall = Bins + 0.1;
+   for (double overflow : {PositiveInfinity, NaN, OverflowLarge, OverflowSmall}) {
+      auto linIndex = axis.ComputeLinearizedIndex(overflow);
+      EXPECT_EQ(linIndex.fIndex, Bins + 1);
+      EXPECT_TRUE(linIndex.fValid);
+      linIndex = axisNoFlowBins.ComputeLinearizedIndex(overflow);
+      EXPECT_EQ(linIndex.fIndex, Bins + 1);
+      EXPECT_FALSE(linIndex.fValid);
+   }
+}
diff --git a/hist/histv7/test/hist_test.hxx b/hist/histv7/test/hist_test.hxx
new file mode 100644
index 0000000000000..c36ba8a722432
--- /dev/null
+++ b/hist/histv7/test/hist_test.hxx
@@ -0,0 +1,12 @@
+#ifndef hist_test
+#define hist_test
+
+#include <ROOT/RRegularAxis.hxx>
+#include <ROOT/RVariableBinAxis.hxx>
+
+#include "gtest/gtest.h"
+
+using ROOT::Experimental::RRegularAxis;
+using ROOT::Experimental::RVariableBinAxis;
+
+#endif
diff --git a/hist/histv7/test/hist_variable.cxx b/hist/histv7/test/hist_variable.cxx
new file mode 100644
index 0000000000000..1b4782c2249f8
--- /dev/null
+++ b/hist/histv7/test/hist_variable.cxx
@@ -0,0 +1,111 @@
+#include "hist_test.hxx"
+
+#include <limits>
+#include <vector>
+
+TEST(RVariableBinAxis, Constructor)
+{
+   static constexpr std::size_t Bins = 20;
+   std::vector<double> bins;
+   for (std::size_t i = 0; i < Bins; i++) {
+      bins.push_back(i);
+   }
+   bins.push_back(Bins);
+
+   RVariableBinAxis axis(bins);
+   EXPECT_EQ(axis.GetNumNormalBins(), Bins);
+   EXPECT_EQ(axis.GetTotalNumBins(), Bins + 2);
+   EXPECT_TRUE(axis.HasFlowBins());
+
+   axis = RVariableBinAxis(bins, /*enableFlowBins=*/false);
+   EXPECT_EQ(axis.GetNumNormalBins(), Bins);
+   EXPECT_EQ(axis.GetTotalNumBins(), Bins);
+   EXPECT_FALSE(axis.HasFlowBins());
+}
+
+TEST(RVariableBinAxis, Equality)
+{
+   static constexpr std::size_t Bins = 20;
+   std::vector<double> binsA;
+   for (std::size_t i = 0; i < Bins; i++) {
+      binsA.push_back(i);
+   }
+   binsA.push_back(Bins);
+
+   std::vector<double> binsB;
+   for (std::size_t i = 0; i < Bins / 2; i++) {
+      binsB.push_back(i);
+   }
+   binsB.push_back(Bins / 2);
+
+   std::vector<double> binsC;
+   for (std::size_t i = Bins / 2; i < Bins; i++) {
+      binsC.push_back(i);
+   }
+   binsC.push_back(Bins);
+
+   const RVariableBinAxis axisA(binsA);
+   const RVariableBinAxis axisANoFlowBins(binsA, /*enableFlowBins=*/false);
+   const RVariableBinAxis axisA2(binsA);
+   const RVariableBinAxis axisB(binsB);
+   const RVariableBinAxis axisC(binsC);
+
+   EXPECT_TRUE(axisA == axisA);
+   EXPECT_TRUE(axisA == axisA2);
+   EXPECT_TRUE(axisA2 == axisA);
+
+   EXPECT_FALSE(axisA == axisANoFlowBins);
+
+   EXPECT_FALSE(axisA == axisB);
+   EXPECT_FALSE(axisA == axisC);
+   EXPECT_FALSE(axisB == axisC);
+}
+
+TEST(RVariableBinAxis, ComputeLinearizedIndex)
+{
+   static constexpr std::size_t Bins = 20;
+   std::vector<double> bins;
+   for (std::size_t i = 0; i < Bins; i++) {
+      bins.push_back(i);
+   }
+   bins.push_back(Bins);
+
+   const RVariableBinAxis axis(bins);
+   const RVariableBinAxis axisNoFlowBins(bins, /*enableFlowBins=*/false);
+
+   // Underflow
+   static constexpr double NegativeInfinity = -std::numeric_limits<double>::infinity();
+   static constexpr double UnderflowLarge = -static_cast<double>(Bins);
+   static constexpr double UnderflowSmall = -0.1;
+   for (double underflow : {NegativeInfinity, UnderflowLarge, UnderflowSmall}) {
+      auto linIndex = axis.ComputeLinearizedIndex(underflow);
+      EXPECT_EQ(linIndex.fIndex, Bins);
+      EXPECT_TRUE(linIndex.fValid);
+      linIndex = axisNoFlowBins.ComputeLinearizedIndex(underflow);
+      EXPECT_EQ(linIndex.fIndex, Bins);
+      EXPECT_FALSE(linIndex.fValid);
+   }
+
+   for (std::size_t i = 0; i < Bins; i++) {
+      auto linIndex = axis.ComputeLinearizedIndex(i + 0.5);
+      EXPECT_EQ(linIndex.fIndex, i);
+      EXPECT_TRUE(linIndex.fValid);
+      linIndex = axisNoFlowBins.ComputeLinearizedIndex(i + 0.5);
+      EXPECT_EQ(linIndex.fIndex, i);
+      EXPECT_TRUE(linIndex.fValid);
+   }
+
+   // Overflow
+   static constexpr double PositiveInfinity = std::numeric_limits<double>::infinity();
+   static constexpr double NaN = std::numeric_limits<double>::quiet_NaN();
+   static constexpr double OverflowLarge = static_cast<double>(Bins * 2);
+   static constexpr double OverflowSmall = Bins + 0.1;
+   for (double overflow : {PositiveInfinity, NaN, OverflowLarge, OverflowSmall}) {
+      auto linIndex = axis.ComputeLinearizedIndex(overflow);
+      EXPECT_EQ(linIndex.fIndex, Bins + 1);
+      EXPECT_TRUE(linIndex.fValid);
+      linIndex = axisNoFlowBins.ComputeLinearizedIndex(overflow);
+      EXPECT_EQ(linIndex.fIndex, Bins + 1);
+      EXPECT_FALSE(linIndex.fValid);
+   }
+}