How to Read Mathematical Descriptions

Look at the description and classify each symbol into one of these categories: a literal (such as number 3 or equality sign), a variable or a syntactic separator (such as parentheses, braces, brackets or the dot between function the parameter and the body of a function in the lambda calculus).

For each variable, determine its domain (i.e. whether it stands for a formula, a type/term, a member of a particular set, a relation or a more complicated structure). The domains can be deduced from the context (either explicitly or implicitly).

Do the same for the whole description.

Now, you have a syntactic tree of the whole description. Check, whether each node of the tree has suitable of children (e.g. whether you are comparing two terms, not a term and a formula). If not, try to fine-tune your previous guesses. If it doesn't help, start over. If it doesn't help, it's time to get back to textbook.

Congratulations, you have a semantically valid parse of the description. Now you can start thinking about its meaning.