MIND, LANGUAGE AND REALITY (Cambridge Univ Press, 1975)

The same mental state may be implemented by different physical states.
Putnam imagines a world called "Twin Earth" exactly like Earth in every respect except that the stuff which appears and behaves like water, and is actually called "water", on Twin Earth is a chemical compound XYZ. If one Earth and one Twin Earth inhabitant, identical in all respects, think about "water", they are thinking about two different things, while their mental states are absolutely identical. Therefore the content of a concept depends on the context ("externalism"). Meanings are not in the mind, they also depend on the objects that the mind is connected to.
Putnam classifies mental states based on their function, i.e. their causal roles withing the mental system, regardless of their physical structure. Putnam originally suggested that the psychological state of an individual be identified with the state of a Turing machine. A psychological state would cause other psychological states according to the machine's operations. Belief and desire correspond to formulas stored in two registers of the machine. Appropriate algorithms process those contents to produce action.

REASON, TRUTH AND HISTORY (Cambridge Univ Press, 1981)

Putnam provides a formal proof that model-theoretic semantics fails as a theory of meaning, because he found a fundamental contradiction between the definition of meaning in model theory (a function which assigns a truth value to a sentence for all possible cases) and the constraint that the meaning of the parts cannot be changed without changing the meaning of the whole. Putnam proves that meaning does not stand in the realtionship between symbols and the world.
His criticism of symbol systems is based on the observation that, since we are part of reality, there can be no complete and true description of the world: we are part of the reality that we observe, we cannot claim the role of independent observer.
The definition of truth depends on the meaning of the words of the language and each definition of truth should list all conditions that meaning depends on (including the definition of truth which is being defined).

REPRESENTATION AND REALITY (MIT Press, 1988)

Putnam abandons his functionalist theory of the brain.
Mind cannot comprehend itself. An automaton cannot explain its own behavior. The same mental state may be implemented by different computational (functional) states, therefore mental states cannot be computer programs.
Explanation and prediction of intentional phenomena such as belief and desire belong to the realm of interpretation: concepts do not exist in the mind, are the output of interpretation. Interpretation can be "normative", when it employs Davidson's principle of charity or Dennett's principle of "rationality", which state that an organism behaves as it should given the circumstances (most of its beliefs are true, it believes in the implications of its beliefs, no two beliefs contradict each other, and so on); or "projective" (Stitch), when it attributes to an organism the propositional attitudes that we would have were we in its situation.
Meaning exhibits an identity through time but not in its essence (such as momentum, which is a different thing for Newton and Einstein but expresses the same concept). An individual's concepts are not scientific and depend on the environment. Most people know what gold is, and still they cannot explain what it is and even need a jeweler to assess whether something is really gold or a fake. Still, if some day we found out that Chemistry has erred in counting the electrons of the atom of gold, this would not change what it is. The meaning of the word "gold" is not its scientific definition, but the social meaning that a community has given it. It is not true that every individual has in its mind all the knowledge needed to understand the referent of a word. There is a subdivision of competence among human beings and the referent of a word is due to their cooperation. Meaning is not in the mind.