Linen
A fabric made from the flax plant. It comes in a white or off white colouring. Linen doesn't take dye well (except blue dye from woad), so most linen was used bleached white or off white.
There is also some mention of "blackened linen" in some period texts, generally as a material used for making armour (specifically gambesons). It is assumes that this is some kind of waterproof material (used by sailors etc), but no-one is sure exactly how the linen was blackened (tar, pitch, charcoal, a bog).
Linen was generally used to make underwear for both men and women, as well as to line outer garments usually made from wool were used for outer layers. Silk was used for outer garments as well, and also linings depending on when and where you are talking about.
Linen is cool in summer (cooler than almost any other natural fibre) and warmer in winter than cotton. You can tell real linen in the shops - crinkle it up in your hand, then release it. Cottons will have a few creases, but linen will have lots. Linen will also feel a lot cooler on warm days to your hands, and will quickly warm up to your hands on cool days.
Some people think that newly purchased linen tends to shrink a lot, so make sure you prewash and dry it at a slightly higher temperature than you will normally use, once or twice before you cut out garments from it. Linen used in period garb doesn't need dry cleaning or ironing - after a few washes it will get softer and most creases will fall out.