Sort[list] sorts the elements of list into canonical order. Sort[list, p] sorts using the ordering function p.

Partition[list, n] partitions list into non-overlapping sublists of length n. Partition[list, n, d] generates sublists with offset d. Partition[list, {n_1, n_2, ...}] ...

Finding elements that match a pattern. This gives the elements of the list which match the pattern x^_. Here is the total number of elements which match the pattern.

Basic plotting functions. This plots a graph of sin(x) as a function of x from 0 to 2π. You can plot functions that have singularities. Mathematica will try to choose ...

Importing and exporting lists and tables of data. This exports a list of data to the file out1. Here are the contents of the file.

Insert[list, elem, n] inserts elem at position n in list. If n is negative, the position is counted from the end. Insert[expr, elem, {i, j, ...}] inserts elem at position {i, ...

Ordering[list] gives the positions in list at which each successive element of Sort[list] appears. Ordering[list, n] gives the positions in list at which the first n elements ...

Mathematica provides several convenient methods for extracting and manipulating parts of matrices. The flexible [[ ]] (Part) and ;; (Span) syntaxes provide compact yet ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

Map[f, expr] or f /@ expr applies f to each element on the first level in expr. Map[f, expr, levelspec] applies f to parts of expr specified by levelspec.