**Author:** Konstantin Makarychev

Approximation algorithms are used to find approximate solutions to problems that cannot be solved exactly in polynomial time. I will talk about linear programming (LP) and then semidefinite programming (SDP) based approximation algorithms. I will give examples of such algorithms and prove their correctness. Then, we will discuss the connection between approximation algorithms and high dimensional geometry. I will also talk about the Unique Games Conjecture and the limits of approximability.