diff --git a/docs/lecture02.ipynb b/docs/lecture02.ipynb
index c092013..4da8c93 100644
--- a/docs/lecture02.ipynb
+++ b/docs/lecture02.ipynb
@@ -2,7 +2,13 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "# Lecture 2 – Kinematics and Lorentz Transformations"
    ]
@@ -119,14 +125,11 @@
    },
    "source": [
     "<!-- In the case of the scattering happens in the x-z plane for both frames, the two frames are related by a boost along the z axis. -->\n",
-    "When we have a final state with two particles ($n=2$), we can define one $xz$ plane that is spanned by the momenta of the two final state particles in the Lab frame. The CoM frame and the Lab frame can now be related by a boost along the $z$-axis (the direction of particle $a$).\n",
+    "When we have a final state with two particles ($n=2$), we can define one $x-z$ plane that is spanned by the momenta of the two final state particles in the Lab frame. The CoM frame and the Lab frame can now be related by a boost along the $z$-axis (the direction of particle $a$).\n",
     "\n",
     "With this definition of the x-z plane, we have:\n",
     "- $\\vec{z}$ is parallel to the beam $\\vec{p}_a$\n",
-    "- $\\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$\n",
-    "\n",
-    "<!-- $ \\vec{z}$ is parallel to the beam $\\vec{p}_a $\n",
-    "$ \\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$ -->"
+    "- $\\vec{y} $ is parallel to $ \\vec{p}_a \\times \\vec{p}_1$"
    ]
   },
   {
@@ -144,9 +147,15 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "Boost and Rotation."
+    "The Lorentz transformation, which includes both boosts (velocity changes) and rotations, is crucial for understanding how the properties of particles, such as position and time, transform between different inertial frames in relative motion."
    ]
   },
   {
@@ -164,14 +173,26 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
-    "Only the energy and the z component change"
+    "Only the energy and the $z$ component of the four-momenta changes, so we can write the Lorentz boost with a 2D matrix."
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "$$\\begin{pmatrix}\n",
     " E^*\n",
@@ -242,16 +263,28 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "$$\n",
-    "\\gamma \\beta = \\frac{E^*_b}{m_b}\n",
+    "\\gamma \\beta = \\frac{E^*_b}{m_b}.\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "We check that it brings the target at rest in Exercise below"
    ]
@@ -268,7 +301,7 @@
    "source": [
     ":::{exercise}\n",
     ":label: boost-exercise\n",
-    "Check that it brings the target at rest\n",
+    "Check that the above boost definition brings the target at rest in the lab frame.\n",
     ":::"
    ]
   },
@@ -285,7 +318,7 @@
     ":::{solution} boost-exercise\n",
     ":class: dropdown\n",
     "\n",
-    "By the boost from CoM frame to Lab frame, and apply if to the 4-vector of particle b (target)\n",
+    "From CoM frame to Lab frame, we apply the boost to the 4-vector of particle b (target)\n",
     "\n",
     "\n",
     "$$\\begin{pmatrix}\n",
@@ -347,7 +380,13 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
    "source": [
     "<!-- By the boost from CoM frame to Lab frame, and apply if to the 4-vector of particle b (target) -->"
    ]