diff --git a/docs/notebooks/twirling.ipynb b/docs/notebooks/twirling.ipynb
index 8dc822f..92bfc11 100644
--- a/docs/notebooks/twirling.ipynb
+++ b/docs/notebooks/twirling.ipynb
@@ -24,6 +24,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## What is twirling?\n",
+    "```\n",
+    "Missing scientific/theoretical explanation\n",
+    "```\n",
     "Let us begin by introducing an auxiliary class `PauliTwirl`, to represent a single Pauli twirl:"
    ]
   },
@@ -91,6 +95,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Operation-preserving twirls\n",
+    "```\n",
+    "Missing scientific/theoretical explanation\n",
+    "```\n",
     "Next we will create a helper function `generate_pauli_twirls` to compute all operation-preserving twirls for a given unitary matrix numerically:"
    ]
   },
@@ -130,7 +138,11 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Finally, with these tools, we can create a simple transpiler pass `TwoQubitPauliTwirlPass` to apply Pauli twirling to an input `DAGCircuit`:"
+    "## Random twirling\n",
+    "```\n",
+    "Missing scientific/theoretical explanation\n",
+    "```\n",
+    "Finally, with these tools, we can create a simple [transpiler pass](https://docs.quantum.ibm.com/transpile/custom-transpiler-pass#transpiler-passes) `TwoQubitPauliTwirlPass` to apply Pauli twirling to an input `DAGCircuit`:"
    ]
   },
   {
@@ -187,6 +199,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "## Usage\n",
     "Using Qiskit's `PassManager` we can now run a simple example:"
    ]
   },