This book provides an updated introductory textbook on the topic of locally convex topological vector spaces. Readers who enjoy combinations of topology, analysis and linear algebra will discover fascinating relevance in this work. The target audience is anyone, such as graduate students and researchers who have a typical background in one semester courses in topics like topology, and analysis of normed/Banach spaces. Several chapters are standard, with topics like basic properties of topological vector spaces and local convexity, the Hahn-Banach Theorem, the basics of duality, and some deep results such as the Banach-Steinhaus and Closed Graph theorems. Unique features of this book include the inclusion of examples from normed and Banach spaces that show how such spaces fit in within the larger context of locally convex spaces, the utility of sequences and series, examples of recent applications to results such as in distribution theory and optimization, and introductions to some atypical contexts of locally convex spaces such as convergence vector spaces and abstract duality pairs. Readers will find a colorful world of spaces and results that will be useful for starting research, or gaining insight into analysis and topology.