A new measure of the complexity of a book-embedding of a simple undirected graph, the number of vertex types in the embedding, is studied. The type of a vertex $v $ in a p-page book-embedding is the $p \times 2$ matrix of nonnegative integers \[ \tau (v ) = \begin{pmatrix} L_1 & & R_1 \\ L_2 & & R_2 \\ & \vdots & \\ L_P & & {R_P } \end{pmatrix}, \] where $L_i $; (respectively, $R_i $) is the number of edges incident to $v $ that connect on page i to vertices lying to the left (respectively, to the right) of $v $. The number of types in a book-embedding relates to the amount of logic necessary to realize fault-tolerant arrays of processors using one specific design methodology. Three sorts of issues regarding vertex types in book-embeddings are studied. A number of techniques for bounding the type-numbers of a variety of graphs are developed; the relationships between typenumber and other graph properties, such as book thickness, are investigated; and the problem of minimizing the typenumber of a graph is ...