6Optimization is an integral part of engineering today. It can eliminate guesswork and help solve complex engineering problems in minutes. This text is an introduction to optimization through baby-steps. Intended audience includes senior undergraduate students, junior graduate students and practicing engineers. No prior background in optimization or programming is assumed. This text covers three complementary topics: (1) optimization theory, (2) numerical methods, and (3) applications. On the first topic, we will recall basic results from single-variable calculus and extend these to higher dimensions. Critical theorems are summarized and illustrated through examples.The second topic of numerical methods lies at heart of optimization. The text encourages the reader to implement one or more optimization methods before delving into Matlab's optimization toolbox. This will provide a better understanding on how optimization algorithms work (or sometimes fail!). Finally, it is the author's opinion that optimization concepts are best understood within the context of an application. We will largely focus here on geometric and structural applications. The latter includes finite-element-based shape optimization using SolidWorks, where we will learn to modify feature dimensions of SolidWorks models, carry out finite element analysis, and optimize, all from within the comfort of Matlab.