Before trying to organize the Perl operators, let's speak a little about what we mean by operator in a programming language. The operators work with numbers and strings and manipulate data objects called operands. We found the operators in expressions which we need to evaluate.
On the other side, we use Perl operators in a certain context. We have two types of contexts: the scalar context which is invoked when Perl is expected to return a single value (like the addition of two numbers) and the list context when Perl is expected to return two or more values. The great majority of the Perl operators work in scalar context, if not we will specify.
Also note that you must be aware of the Perl operators precedence, if you are not sure, it is better to use the brackets.