  In a pair of recent papers (one to appear and one forthcoming), the author
develops a general version of small cancellation theory applicable in higher
dimensions, and then applies this theory to the Burnside groups of sufficiently
large exponent. The present article gives a brief introduction to the methods
and techniques involved in the proofs. Many of the ideas originate with the
recent work of A. Yu. Olshanskii and S. V. Ivanov. Some familiarity with their
work on the Burnside problem is assumed.
