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Thevenin's Theorem

Any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a single voltage source (VthV_{th}) in series with a single impedance (ZthZ_{th}).
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The statement of the theorem

Let N\mathcal{N} be a linear, passive, two-terminal electrical network defined by its admittance matrix Y∈RN×N\mathbf{Y} \in \mathbb{R}^{N \times N}, where NN is the number of nodes. Let aa and bb be the designated terminals. The current I\mathbf{I} and voltage V\mathbf{V} at the nodes satisfy the linear relationship I=YV+Isources\mathbf{I} = \mathbf{Y} \mathbf{V} + \mathbf{I}_{sources}.\n\begin{enumerate}\n \item The open-circuit voltage VthV_{th} is defined as the voltage across terminals aa and bb when the net current flow is zero: Vth=Vab∣Iab=0V_{th} = V_{ab} \Big|_{\mathbf{I}_{ab}=0}.\n \item The equivalent Thevenin resistance RthR_{th} is defined by the ratio of the open-circuit voltage to the current injected by a test source Itest\mathbf{I}_{test} applied across aa and bb, assuming all internal sources are deactivated (i.e., Y\mathbf{Y} is derived from a source-free network): \n R_{th} = \frac{V_{ab}(\mathbf{I}_{test})}{\mathbf{I}_{test}} \quad \text{where } \mathbf{I}_{test} = \frac{V_{ab}(\mathbf{I}_{test})}{R_{th}} \text{ and } V_{ab}(\mathbf{I}_{test}) = \text{Voltage across } a, b \text{ due to } \mathbf{I}_{test}.\n\end{enumerate}\nThe theorem asserts that the network $\mathcal{N}$ is equivalent to a simple series circuit $\mathcal{N}_{eq}$ characterized by the voltage source $V_{th}$ and resistance $R_{th}$, such that for any applied terminal current $\mathbf{I}_{load}$, the voltage $V_{ab}$ satisfies:\n\mathbf{V}_{ab} = V_{th} - R_{th} \mathbf{I}_{load}$$
Source: Wikipedia