Conventions

Write as few parentheses as possible:

$$(\lambda y.(xy)) = \lambda y.xy$$

Application associates to the left:

$$xyz = ((xy)z)$$

Abstractions bind as far as possible to the right:

$$\lambda x.(\lambda y.y)x = (\lambda x.((\lambda y.y)x))$$

Abstractions can be abbreviated:

$$\lambda x.\lambda y.M = \lambda xy.M$$

A lambda term in Haskell syntax:

\x -> M

...is the same as: $\lambda x.M$