1. Critical analysis is the process of dividing into sub-parts and analysing another's claims to consider: what concepts (ideas) they are based on (true or false or uncertain); how far they agree with the available evidence; and how logical the structure of the argument used to present them is.
   See What is Critical Analysis? (in detail)

2. A Claim, in academic terms, is something that is asserted to be true or valid, and which must be based on factual evidence. Academics critically analyse and evaluate the evidence upon which claims are based.
   See What is Critical Analysis? (in detail)

3. Argument is the process of putting together and linking evidence to support or reject a claim.
   Academic writing is based around argument, which includes the logic structure used to hold a text together.
   See What is an Argument? (in detail)

4. Opinion, in academic terms, is the judgement or viewpoint reached after analysing, assessing and evaluating arguments, claims and evidence. Academic opinion is objective, like that of a judge who weighs the evidence (for and against) and judges each case on its merits. (Personal opinion which is based on beliefs or codes of ethics, rather than evidence, is not acceptable in academic terms as it cannot be tested in the same way.)
   See What is Opinion? (in detail)

5. 1. A hypothesis (plural hypotheses) is an explanation for something based on known facts but which has not yet been definitely proved to be true.

      For example, it is hypothesised that humans can contract the human form of BSE (mad cow disease) through eating meat not just infected cows but from other animals that have eaten infected cows or through the milk of infected cows. We have some evidence for this but it is not yet sufficient for the case to be considered proven. A hypothesis gives the basis for further tests to be carried out. The results may or may not support the hypothesis.

   2. A hypothesis can also be used as the basis for further reasoning.
      For example, if water once existed on the moon - as several scientists have hypothesised - then life in some form is likely to have existed on the moon.

      A hypothesis thus, tends to have conceptual links with the future, either in terms of the discovery of new information or in terms of progressing ideas.

6. A theory is a set of reasoned ideas intended to explain facts or events.
   For example, Darwin's theory of evolution. Often two or more theories exist to explain the same set of circumstances, for example, Big Bang versus Steady State theory in Physics. Theory is often contrasted with practice. Theory refers to ideas or suppositions and practice refers to what actually happens, events.

   In some cases, theory is used more generally to refer to a set of ideas.
   For example, economic theory, music theory.

   In conceptual terms, a theory links back to the past, either as an explanation of already existing facts or to refer to an existing body of knowledge (which may, of course, be added to).

See also: What is Critical Analysis? (in detail) for examples of:
premise
necessary and sufficient conditions