The course aims on introducing some of the most important quantum invariants of knots/links and 3-manifolds, including the Jones and colored Jones polynomials, the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants, and their underlying topological quantum field theories (TQFT's). In this course, I will use the skein theoretical approach to the theory which needs the minimum prerequisites (linear algebra), and emphasize the relationship with the geometric structures of the manifolds. The course will be related to but independent from the course offered in Spring 2018 by E. Rowell and in Fall 2018 by JM Landsberg on Quantum Computation.