diff --git a/book/src/SUMMARY.md b/book/src/SUMMARY.md
index f5a19ff..930d34a 100644
--- a/book/src/SUMMARY.md
+++ b/book/src/SUMMARY.md
@@ -19,6 +19,7 @@
     - [Circuit commitments](design/proving-system/circuit-commitments.md)
     - [Vanishing argument](design/proving-system/vanishing.md)
     - [Multipoint opening argument](design/proving-system/multipoint-opening.md)
+    - [Inner product argument](design/proving-system/inner-product.md)
     - [Comparison to other work](design/proving-system/comparison.md)
   - [Implementation](design/implementation.md)
   - [Gadgets](design/gadgets.md)
diff --git a/book/src/design/proving-system/inner-product.md b/book/src/design/proving-system/inner-product.md
new file mode 100644
index 0000000..185fbf4
--- /dev/null
+++ b/book/src/design/proving-system/inner-product.md
@@ -0,0 +1,11 @@
+# Inner product argument
+
+Halo 2 uses a polynomial commitment scheme for which we can create polynomial commitment
+opening proofs, based around the Inner Product Argument.
+
+> TODO: Explain Halo 2's variant of the IPA.
+>
+> It is very similar to $\text{PC}_\text{DL}.\text{Open}$ from Appendix A.2 of [BCMS20].
+> See [this comparision](comparison.md#bcms20-appendix-a2) for details.
+>
+> [BCMS20]: https://eprint.iacr.org/2020/499