Optimization theory : a concise introduction Mathematical preparations Optimization problems and existence of optimal solutions Necessary and sufficient conditions of optimal solutions Problems with convexity and quasi convexity conditions Linear programming Mathematically most of the interesting optimization problems can be formulated to optimize some objective function subject to some equality and or inequality constraints. This book introduces some classical and basic results of optimization theory including nonlinear programming with Lagrange multiplier method the Karush Kuhn Tucker method Fritz Johns method problems with convex or quasi convex constraints and linear programming with geometric method and simplex method. A slim book such as this which touches on major aspects of optimization theory will be very much needed for most readers. We present nonlinear programming convex programming and linear programming in a self contained manner. This book is for a one semester course for upper level undergraduate students or first second year graduate students. It should also be useful for researchers working on many interdisciplinary areas other than optimization