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Michael Hutchings' lecture notes was were precisely for this purpose(; posted on his webpage)webpage: http://math.berkeley.edu/~hutching/

Lecture Notes on Morse Homology (with With an Eye Towards Floer Theory and Pseudoholomorphic Curves)

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Michael Hutchings' lecture notes was precisely for this purpose (posted on his webpage):

Lecture Notes on Morse Homology (with an Eye Towards Floer Theory and Pseudoholomorphic Curves)