In the endeavor to design and implement useful quantum computers, various platforms haveseen varying levels of success, and the route to the era of fully scalable quantum computing remains shrouded in mystery. One such platform for quantum computation is superconducting circuits, which are a fruitful environment for the observation of quantum physics on mesoscopic scales. In any effort to characterize the quantum behavior of superconducting circuits, a classical theory of circuits with a straightforward route to quantization is necessary. In this thesis, we approach the problem of establishing a maximally general theory of circuits. First, we formalize a framework wherein a classical Hamiltonian may be derived for an arbitrary nondissipative circuit, assuming only that Kirchhoff’s laws admit a unique solution. We also provide an algorithm for deriving such Hamiltonians, and prove that it may always be executed successfully for nonsingular circuits. Secondly, we generalize the aforementioned framework in such a way that circuit duality is manifestly a relabeling transformation while providing novel insight into the ill–behaved properties of nonplanar circuit duals. Finally, we produce an even more general framework that captures the classical behavior of even dissipative circuits, including a formal argument that Johnson–Nyquist noise applies to all linear resistors and a derivation of Johnson–Nyquist noise for nonlinear resistors. We derive a principle of least action from which one may derive Langevin and Fokker–Planck equations describing the dynamics of circuits with linear and nonlinear dissipative elements alike.