This course provides a complete and practical understanding of optimization techniques used in machine learning, deep learning, and artificial intelligence. The course is carefully designed to explain optimization algorithms from fundamental concepts to advanced adaptive learning rate optimizers using step-by-step mathematical derivations, intuitive explanations, flowcharts, convergence analysis, and practical implementations. Learners will begin with the basics of optimization, learning rates, gradients, error minimization, and regression modeling. The course gradually introduces batch gradient descent, stochastic gradient descent (SGD), and mini-batch gradient descent and moves toward advanced optimizers such as AdaGrad, RMSProp, AdaDelta, ADAM, ADAMAX, and NADAM. A major focus of this course is understanding how adaptive learning rate strategies improve convergence and optimization efficiency. Learners will learn concepts such as first moment estimation, second moment estimation, bias correction, adaptive parameter updates, gradient sensitivity, convergence behavior, oscillation analysis, and stability of optimizers. The course also includes practical implementations using MATLAB and Python, allowing learners to build optimization algorithms from scratch. Students will analyze convergence plots, compare optimizer performance, and understand why certain optimizers perform better in different situations. In addition to theory and coding, the course includes professionally designed flowcharts, algorithmic workflows, mathematical derivations, numerical examples, and Udemy-style practice questions to strengthen conceptual understanding. By the end of this course, learners will have a strong foundation in modern optimization algorithms and will be able to confidently apply them to machine learning and deep learning problems.