If you feel something is missing from the list, please use the Course Forum to point this out, and possibly suggest a notation. I will then add it to the list.

x1, x2, xn   - x with subscripts 1, 2, n
a /= b       - a not equal to b
a <= b       - a smaller than or equal to b
a >= b       - a greater than or equal to b
oo           - infinity
INF          - infinity

0            - empty set
A U B        - A union B
A /\ B       - A intersection B ("snitt")
A `snitt` B  - A intersection B ("snitt")
A \ B        - A difference B
A -> B       - functions from A to B
A x B        - Cartesian product of A and B

𝔹           - set of booleans {0,1}
ℕ           - natural numbers
ℤ           - integer numbers ("heltal")
ℕ+, ℤ+     - positive integers ("positiva heltal")
ℚ           - rational numbers
ℝ           - real numbers

A <= B       - A subset of B
A < B        - A strict subset of B

Note: When you use x for Cartesian product, please do not use x as a variable name at the same time.

f : ℕ -> ℕ - f goes from ℕ to ℕ
x |-> 2x     - the function that takes x to 2x
a*b          - multiplication
a^b          - a to the power of b ("a upphöjd till b" / "potens")
f . g        - function composition of f and g

p ^ q        - conjunction
p /\ q       - conjunction
p & q        - conjunction
p v q        - disjunction
p \/ q       - disjunction
p -> q       - implication
p <-> q      - equivalence
~p           - negation ("inte")
not p        - negation ("inte")
inte p       - negation ("inte")

ALL x : P(x)   - for all x, such that P(x)
EXI x : P(x)   - exists x, such that P(x) ("det finns ett x")
FINNS x : P(x) - exists x, such that P(x) ("det finns ett x")

SUM(i=0,n) ai   - the sum of all ai for i from 0 to n
oo              - infinity
INF             - infinity