The purpose of this paper is to give the reader an impression of various techniques used in controlled algebra. Controlled algebra was introduced by ConnellHollingsworth and developed by Quinn [4, 10] in connection with foundational studies in topological manifold theory. Suppose given a ring R and a space X, possibly with some extra structure such as a metric. The objects studied in controlled algebra are free based R-modules together with a map π from the basis to the metric space X. One… CONTINUE READING