The book presents a graduate level, rigorous, and self-contained introduction to linear optimization (LO), the presented topics being

1. expressive abilities of LO;
2. geometry of LO - structure of polyhedral sets, LO duality and its applications;
3. traditional LO algorithms - primal and dual simplex methods, and network simplex method;
4. polynomial time solvability of LO via ellipsoid algorithm;
5. conic programming with emphasis on expressing abilities of second order and semidefinite optimization, and polynomial time primal-dual interior point algorithms for linear and semidefinite optimization.