Arising from the 1996 Cape Town conference in honour of the mathematician Bernhard Banaschewski , this collection of 30 refereed papers represents current developments in category theory, topology, topos theory, universal algebra, model theory, and diverse ordered and algebraic structures. Banaschewski's influence is reflected here, particularly in the contributions to pointfree topology at the levels of nearness, uniformity, and asymmetry. The unifying theme of the volume is the application of categorical methods. The contributing authors are: D. Baboolar , P. Bankston , R. Betti , D. Bourn , P. Cherenack , D. Dikranjan/H.-P. Künzi , X. Dong/W. Tholen , M. Erné, T.H. Fay , T.H. Fay/S.V. Joubert , D.N. Georgiou/B.K. Papadopoulos , K.A. Hardie/K.H. Kamps/R.W. Kieboom , H. Herrlich/A. Pultr , K.M. Hofmann , S.S. Hong/Y.K. Kim , J. Isbell , R. Jayewardene/O. Wyler , P. Johnstone , R. Lowen/P. Wuyts , E. Lowen-Colebunders/C. Verbeeck , R. Nailana , J. Picado , T. Plewe , J. Reinhold , G. Richter , H. Rörl , S.-H. Sun , Tozzi/V. Trnková, V. Valov/D. Vuma , and S. Veldsman . Audience: This volume will be of interest to mathematicians whose research involves category theory and its applications to topology, order, and algebra.