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
Probability 

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 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
 Sets, set theory and cardinality
 Combination and permutation
 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.