Morse homolojiler etrafında yolculuk (modern yaklaşım)

This thesis is a workout of the lecture notes of M. Hutchings on Morse Homology. Our main goal is to study Morse Theory on fi nite dimensional manifolds by adapting the ideas of Floer Theory on infi nite dimensional manifolds. In the fi rst part of the thesis, we give all necessary de finitions from Morse Theory such as Morse functions, moduli spaces and Morse homology. We prove that Morse homology is isomorphic to singular homology. We also study some applications of Morse homology to algebraic topology. Throughout the second part, we investigate Morse-Bott functions, moduli spaces and Morse-Bott homology by giving several examples. Finally, we make use of spectral sequences to simplify the computations of Morse-Bott homology.