This is an introductory lecture in Legendrian contact homology in ℝ^3. We will be following the article ``Legendrian contact homology in ℝ^3" by Etnyre and Ng. We will begin with recalling basics of contact geometry and Legendrian knots.

This is an introductory course on modern Morse theory. We will introduce Morse functions, Morse complex and Morse homology for closed manifolds. We will show invariance properties of the Morse complex and look at applications like Poincare duality.We will try to follow and cover Part I of "Morse theory and Floer homology" by Michèle Audin and Mihai Damian.

This is an introductory course on modern Morse theory. We will introduce Morse functions, Morse complex and Morse homology for closed manifolds. We will show invariance properties of the Morse complex and look at applications like Poincare duality.We will try to follow and cover Part I of "Morse theory and Floer homology" by Michèle Audin and Mihai Damian.