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Probability is a subtle concept that is typically defined in terms of the relative frequency of occurrence of an event, or the degree of belief that the event will occur (or that a statement is true, etc.).

Elementary probability
Sometimes introduced in primary school mathematics classes, the first serious study of the subject is usually undertaken in secondary school or university level courses
Probability theory
Formal, axiomatic study at the university level, based on real analysis and especially measure theory.

Major topics

  • Interpretations of probability
    • Frequentist approach (based on aleatory probability, empirical probability)
    • Bayesian approach (based on epistemic probabilty)
  • Definitions of probability
    • Probability (relative frequency)
    • Axioms of probability (or Probability axioms, a.k.a. Kolmogorov axioms)
    • Cox's theorem
    • Confidence and certainty
  • Odds, expected value and outcome, fair and unfair games
  • Properties of probability
  • Discrete probability versus continuous probability
  • Combinatorics and advanced counting
  • Weighted probability
  • Probability distribution functions
  • Probability density functions
  • Cumulative distribution functions
  • Conditional probability and mutually exclusive events
  • Classical probability and statistics
  • Probability and statistics

See Wikipedia:Probability for more information.