This is the first introduction to an area of research which has grown up in recent years, and which has begun to answer Lethaby's call of nearly seventy years ago for a programme of theoretical work on the geometry of architectural plans. The work attempts to show how, given suitable geometric definitions of certain classes of plans, systematic methods can be devised for enumerating all possible plans of each type. Particular attention is devoted to rectangular room plans, set within rectangular boundaries - so-called rectangular dissections - since the plans of many actual small buildings, especially houses, approximate to this kind of geometrical arrangement. Computer methods are described in some detail. Mathematical techniques are introduced for the representation of plans and their properties, and it is shown how these plan-generating methods, and the catalogues of plans which they can produce, may be applied in three areas: - in design, in building science, and in architectural history.