Several algorithms for generating partitions of positive numbers are given. First, an algorithm for generating all the partitions is given, then algorithms for generating of all partitions in which all terms are smaller than a given n, between n and m, and partitions of n to a given k. Each of the algorithms produces the whole sequence in a time proportional to the length of that sequence; moreover, each new partition is produced in no more than a constant number of steps independent on the parameters of the algorithm.