These are lectures given at the 2019 PCMI Undergraduate Faculty Program. The topic of the lectures was Morse theory and handle bodies.

1. Cobordisms and Morse Functions.
2. Handlebody Decompositions.
3. Surfaces (Kirby pictures, classification, and diffeomorphisms).
4. H-cobordism theorem.
5. Heegaard Splittings of 3-manifolds.
6. Cerf and Smale Thoery.
7. Extra Lectures
   1. Corners, rounding, glueing, and cutting.
   2. Jet Spaces.
   3. Morse Lemma.