Electric charge is a concept defined rigorously in electrostatics in terms of the properties that matter exhibits when placed in an electromagnetic field. In the case of electric circuits we are mostly interested in the charge going through wires (or entering or exiting the terminal of a component through a specific terminal), which is equal to the number of electrons going through the wire (or entering that terminal), $N$, multiplied by the charge of a single electron $N\times 1.602\times10^{-19}\:{\textcolor{gray}C}$. The SI unit of charge is the coulomb (${\textcolor{gray}C}$).

The electric current going through a wire is defined as the charge that goes thought that wire in unit time $$\begin{equation}i(t)=\frac{dQ}{dt}\end{equation}$$ The SI unit of electric current is the ampere or amp (${\textcolor{gray}A}$). The conventional symbol for current is $I$ (see Fig. 1), which originates from the French phrase intensité du courant, (current intensity). The $I$ symbol was first used by André-Marie Ampère, after whom the unit of electric current is named.

The current can flow in either of the two directions in a wire. When defining a variable $I$ to represent the current, the direction representing positive current must be specified, usually by an arrow on the wire. This is the reference direction of the current. The actual direction of current through a specific circuit element is usually unknown until the current is computed numerically. Consequently, the reference directions of the currents are often assigned arbitrarily when we start analyzing a circuit. After the circuit is solved, a negative value for the current implies that the actual direction of the current is opposite than that of the reference direction.

If the current is known, one can compute the total charge that goes through the wire from time $t=0$ to $T$ by integrating the previous equation $$\begin{equation}Q(T)=\int_0^T i(t) dt\end{equation}$$

The electric potential, also known as electrostatic potential (or simply potential), is defined rigorously in electrostatics, in terms of the amount of work needed to move a unit charge from an initial point to a reference point (often taken at infinity). In the case of electric circuits the reference point is the ground node and the potential of the ground node is assumed to be $0$. The SI unit of electric potential is the volt (${\textcolor{gray}V}$).

Ideal wires are defined as wires with zero internal resistance. Therefore, the amount of work to move electrons from one point of an wire to another point of the same wire is equal to $0$. In addition, the electric potential of an ideal wire is the same at any point on the wire.

Voltage, also known as (electric) potential difference, is the difference of the electric potential between two points. Therefore, the SI unit of the voltage is the volt (${\textcolor{gray}V}$. If we denote the two points by $A$ and $B$ and the potentials at thsoe two points by $V_A$ and $V_B$, the voltage between the two points is $$\begin{equation}V_{AB}=V_{A}-V_{B}\end{equation}$$ To simplify the notations on circuit diagrams, we often denote point $A$ (the first point) with $+$ and point $B$ (the second point) with $-$ (see Fig. 1). In this case, voltage $V$ is understood to be the voltage from the node denoted with $+$ to the node denoted with $-$.

Finally, using the previous equation it is obvious that $$\begin{equation}V_{AB}=-V_{BA}\end{equation}$$