A privative, named from Latin privare, "to deprive", is a particle that negates or inverts the value of the stem of the word. In Indo-European languages many privatives are prefixes; but they can also be suffixes, or more independent elements.
Privative prefixes 
- un- from West Germanic; e.g. unprecedented, unbelievable
- in- from Latin; e.g. incapable, inarticulate.
- a-, called alpha privative, from Ancient Greek α-, αν-; e.g. apathetic, abiogenesis.
These all stem from a PIE syllabic nasal privative *n̥-, the zero ablaut grade of the negation *ne, i.e. "n" used as a vowel, as in some English pronunciations of "button". This is the source of the 'n' in 'an-' privative prefixed nouns deriving from the Greek, which had both. For this reason, it appears as an- before vowel, e.g. anorexia, anesthesia.
The same prefix appears in Sanskrit, also as a-, an-. In North Germanic languages, the -n- has disappeared and Old Norse has ú- (e.g. ú-dáins-akr), Danish and Norwegian have u-, whereas Swedish uses o, and Icelandic uses the etymologically related ó.
Unfortunately, English in particular is inconsistent in its usage of privatives. One example is the word "invaluable." Following the example above, a non-native English speaker could correctly infer that someone who is "inarticulate" is not articulate. Applying the same rule to other words should be fairly straightforward, but the same person would be erroneously led to believe that that something "invaluable" is not valuable. But the word "invaluable" actually refers to something is extremely valuable or incredibly useful. This is just one of many inconsistencies in the English language. (Although the prefix is not the issue so much as the important, though subtle difference in meaning between "valuable" as an adjective ("having great value") and "valuable" as a form of a verb (expressing the possibility to estimate something's value).)
However, one could infer that the term invaluable refers not to things without value, but to those to which a "value" cannot be assigned: in-value-able. Much in the same way that the verb "to value" could mean either to cherish or to assign a value or price to something (e.g. to value a house, car or antique). Invaluable, then, can draw many parallels with the meaning of the term priceless in this context, and the use of the privative is justified. "Inflammable" is perhaps a more complex example of inconsistencies in English, meaning "flammable" as opposed to "not flammable". It is possible in this case that the "in-" prefix is due to the preposition, rather than the privative, i.e. (to go up) in flames, or simply to inflame.