What are good Morse Theory lecture notes and books?

If you are looking for the classical approach to Morse theory, I feel nothing beats Milnor's book on the subject:

Milnor, J. Morse theory. Annals of Mathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963

For the Morse homological approach, i.e. counting flowlines, I really like Weber's paper on the subject:

Weber, Joa The Morse-Witten complex via dynamical systems. Expo. Math. 24 (2006), no. 2.

Another standard reference is the book of Banyaga and Hurtubise.

Banyaga, Augustin; Hurtubise, David Lectures on Morse homology. Kluwer Texts in the Mathematical Sciences, 29. Kluwer Academic Publishers Group, Dordrecht, 2004.

A book that is tough to read, but is a gateway to Floer theory is Schwarz' book.

Schwarz, Matthias Morse homology. Progress in Mathematics, 111. Birkhäuser Verlag, Basel, 1993.

I heard good things about the book of Audin and Damian, but I have not read it.

Audin, Michèle; Damian, Mihai Morse theory and Floer homology. Translated from the 2010 French original by Reinie Erné. Universitext. Springer, London; EDP Sciences, Les Ulis, 2014.

These lecture notes were actually mainly devoted to the Morse Complex in the infinite dimensional setting; but they were thought to be suitable for finite dimensional manifolds as well (btw, you don't need to pay for them).

Another classic text is Bott's Lectures on Morse theory, old and new.