Centering on the mathematical models and Kirchhoff's Laws that form the foundation of electrical circuit analysis, this study presents the systematic methods required for solving circuit equations from an analytical perspective. Developed based on student feedback from the lecture notes of the "Fundamentals of Electric Circuits" course taught at the ITU Faculty of Electrical and Electronics Engineering, the work distinguishes itself from similar resources with its distinctive technical content, such as graph-based analysis methods and the investigation of non-linear resistive circuits. Combining theoretical knowledge with numerical analysis skills, the book serves as a holistic and modern learning guide for both academic education and engineering applications, thanks to its interactive structure supported by the author's presentations and video content on digital platforms.