Section 5.8 of the book An Introduction to Mathematical Cryptography defines the divisor of a rational function $f(X,Y)$ defined on an elliptic curve $E: Y^2 = X^3 + AX + B$ as the formal sum:
$\text{div}(f) = \sum\limits_{P \in E} n_P [P]$
The positive coefficients $n_P$ correspond to the multiplicity of $P$ as a zero of $f$, and the negative coefficients $n_P$ correspond to the multiplicity of $P$ as a poles of $f$.
The book adds: In this formal sum, the coefficients $n_P$ are integers, and only finitely many of the $n_P$ are nonzero, so $\text{div}(f)$ is a finite sum.
On page 318, it defines sum of a divisor, by dropping the square brackets:
$\text{Sum} \left( \text{div}(f) \right) = \text{Sum} \left( \sum\limits_{P \in E} n_P [P] \right) = \sum\limits_{P \in E} n_P P$
Actually, I don't understand the notation $[P]$. What do the square brackets mean here?