  After a pedagogical review of elementary cosmology, I go on to discuss some
obstacles to obtaining inflationary or accelerating universes in M/String
Theory. In particular, I give an account of an old No-Go Theorem to this
effect. I then describe some recent ideas about the possible r\^ole of the
tachyon in cosmology. I stress that there are many objections to a naive
inflationary model based on the tachyon, but there remains the possiblity that
the tachyon was important in a possible pre-inflationary Open-String Era
preceding our present Closed String Era.
