Notation I use a lot:

• \( \mathbb{Z} \) represents the Integers (Zahlen I think)
• \( \mathbb{Q} \) represents the Rationals (fractions of integers)
• \( \in \) means "in" used for belonging to a set, e.g. \(q \in \mathbb{Q}\)
• \( \forall \) means "for all" or "for every" used like \(\forall x \in \mathbb{Z}\) to say "For all X in the integers" or just "for all integers"
• \( \exists \) means "There exists", normally used like \(\exists x \in \mathbb{Z}\) to say "There exists some X in the integers"
• IFF means "if and only if"
• s.t. means "such that"