This dissertation studies multiple tolerancing problems for multi-featured parts. The minmax point-to-point interference problem studies the ways in which manufacturing tolerances affect the likelihood of meeting composite tolerances, and acceptable fits for mating parts; the least squares point-to-point interference problem studies the ways in which manufacturing tolerances affect Taquchi-type squared-error penalties for failing to meet exact design specifications. A certain extension of extreme value theory is used for the minmax formulation; the least squares formulation involves certain asymptotic aspects of non-linear least squares;Only translation (not rotation) adjustment is used in the minmax problem. The minmax interference is approached by upper- and lower-bounding processes. The extreme value of a Rayleigh distribution is involved in the upper-bounding process, and the diameter of a random convex hull is involved in the lower-bounding process;Rotation is considered in addition in the least squares problem, and the distribution of the optimal adjustment (x*,y*,[theta]*) is provided. The roles of pattern size and location also are explored.