In ths work, new multicomponent feasibility, column design and column sequencing tools are proposed. These tools are particularly useful in the synthesis of distillation columns and column sequences that separate azeotropic mixtures, where they provide accurate design parameters as well as good estimates of product compositions for use in commercial simulators. Recent work on ternary mixtures has led to the development of a new criterion for establishing staged column feasibility. This new criterion provides a necessary and sufficient condition for staged-column feasibility, and a column design method is developed based on this criterion for the design of simple and complex columns. The column design method can be extended to describe non-ideal column operation as well as packed columns. The column design method is particularly useful in the design of columns that separate azeotropic mixtures as it provides accurate column specifications where conventional shortcut methods fail. A retrofit method for increasing throughput is also developed using the new feasibility criterion. A new feasibility test for product compositions from columns separating multicomponent mixtures is introduced. Unlike present methods, the new feasibility test requires only the specification of the principal mole fractions in both products. Visualisation is not required as feasibility is established numerically. The feasibility test is therefore applicable to mixtures with any number of components. The feasibility test is extended to identify feasible and potentially feasible classes of splits, which are defined by product regions instead of product compositions. Various classes of splits are then grouped according to type. A column design method for columns separating multicomponent azeotropic mixtures is developed. Based on a new criterion developed for application in ternary mixtures, the new column design method requires the specification of the principal mole fractions in both products. The design method is developed for two cases - columns that produce pure components and columns that perform general splits. In both cases a matrix of feasible operating parameters can be constructed, which can be used to identify favorouble operating parameters. The feasibility and column design methods are used to develop an algorithmic column sequence synthesis procedure for multi component azeotropic mixtures. Given a feed composition and product requirements, the synthesis procedure makes use of the feasibility test for classes of splits to generate a number of potentially feasible column sequences, each of which has an associated recycle superstructure. Feasible column sequences are then identified and the multi component column design methods are employed for every column in the sequence.