Explore the foundations of contact geometry in this comprehensive lecture from the International Centre for Theoretical Sciences. Delve into key concepts such as the Frobenius theorem, local theory of contact manifolds, contactomorphisms, and the Gray stability theorem. Examine the relationship between contact and symplectic structures, and learn about contact submanifolds of symplectic manifolds. Gain insights into J-holomorphic curves, Gromov-Witten invariants, and their connections to complex algebraic geometry and physics. Progress from introductory material to advanced topics, including lemmas and proofs, to develop a thorough understanding of this important area of mathematics.