This thesis discusses an approach to the problem of making school time-tables with the aid of an electronic digital computer. The mathematical model defined is capable of describing almost all of the features required in the time-table for a normal British Secondary School. Having defined the model a system for helping the school staff to present their data accurately in the required form and a computer program to check this data are discussed. Methods are then described for representing the data and the additional information necessary during the construction of the time-table either inside or outside the computer. The main program, which attempts to make the time-table, makes a sequence of assignments which continues either until a complete solution has been obtained or until the completion of a solution is no longer possible. In the latter case some of the previous assignments are removed and alternative choices made. A qualitative evaluation of the main program is given which shows that in general the methods used are not capable of producing time-tables for real schools since for most real, schools no solution of the type sought exists. The conclusion is that the constraints must be made more flexible and that this can best be achieved by combining the powers of the computer, to perform operations quickly and accurately, with those of the experienced manual time-tabler, to make decisions based on a flexible and ill-defined set of constraints. This could most effectively be achieved by allowing the manual time-tabler to control the computer using an on-line terminal.