These lectures were first given during my tenure of a Walker- Ames Visiting Professorship in the Department of Astronautics and Aeronautics at the University of Washington, November 2-12, 1964. I am grateful for the interest shown there and for the tranquil hospitality of Dr. JOHN BOLLARD and Dr. ELLIS DILL, which allowed me the leisure sufficient to write the first manuscript. I thank Dean ROBERT Roy and Dr. GEORGE BENTON for the unusual honor of an invitation to deliver a series of public lectures at my own university. Apart from the footnotes on pp. 49, 50, and 85, which have been added so as to answer questions allowed by the slower pace of silence, and the obviously necessary note on p. 106, the lectures of this second series are here printed as read, February 9-25, 1965. Thus I may call these, in imitation of a famous example, " Bal timore Lectures". Acknowledgment The first lecture is based largely upon my Bingham Medal Address of 1963, part of which it reproduces verbatim. The filth lecture may be regarded as a partial summary of my course on ergodic theory at the International School of Physics, Varenna, 1960. Much of the last lecture runs parallel to my article "The Modern Spirit in Applied Mathematics", ICSU Review of World Science, Volume 6, pp. 195-205 (1964), and some paragraphs are taken from my address to the Fourth U. S. National Congress of Applied Mechanics (1961).