This page serves to collect excellent online sources for the subject of concept, including concept clarification. It can be expanded later for a broader purpose. See also external links in Wikipedia.
A concept is to be distinguished from a word or phrase. As a first approximation, a concept is a word meaning. Thus, a single word covers multiple concepts, and a single concept is named by multiple words. By means of example, the concept of cat-domestical-animal is named by word "cat" but also by word "grimalkin". And the other way around, the word "cat" covers the concept of cat-domestic-animal but also cat-felid-feline. We use the hyphenated names to unambiguously identify the concepts, hoping that listing a set of synonyms will serve to disambigute. Thus, each WordNet's synset is intended to match a single concept.
Now, why would concept not be a word meaning? It is because concepts seem to exist without words. Thus, pre-linguistic humans were probably able to rank observed individuals, e.g. individual trees, under a quasi-headword. The same is probably true of other primates. Such a sophisticated animal as a chimp cannot operate in their environment without this kind of conceptual ability, the ability to class individual observed objects under classes, and and to interconnect classes by meaningful relationship. Thus, concepts would be some kind of mental objects different from word meaning. It would still be true that words point to concepts, but not each concepts would need to be a word meaning.
Sum of parts concepts are also concepts. Thus, white-cat is also a concept, even if it is just cat that is white. Thus, it would seem any noun phrase ambiguously identifies a concept. Indeed, noun-phrase-that-ambiguously-identified-a-concept is also a concept.
As was pointed above, there is no unique way to name concepts. Thus, we can say cat-domestical-animal or cat-animal-in-the-narrow-sense. The former seems much better.
German is a language with a penchant to form long compounds, providing a closer mapping between concepts and words. By contrast, English has to map between 1) concepts and 2) words and sequences of multiple words on the other hand.
Concepts may also correspond to individual instances, at least to abstract instances. Since, "blueness" is a name of concept, a quality, and that is an individual instance. One may be less ready to consider concepts for individual people or tree as concepts. It is unclear what qualities a concept for, say, Albert Einstein contains: it rather seems that the Kripkean view is of import, that "Albert Einstein" is a rigid designator rather than a package of properties to select by. If one accepts the Russelian theory of names as descriptions, there are also concepts for individual instances, having a certain selection of properties as uniquely identifying these instances. One may object that these concepts are not really belonging to the individuals since they would not belong to them across possible worlds. This needs clarification and discussion.
Concepts can be disjunctive (X or Y or Z), as least as far as classes are concerned. Thus, if we have the concept of star as that which reveals itself as bright dot on the sky, we can classify these into fixed stars, slowly moving stars and falling stars, and the result of that classification are classes. Of course, a class can also have multiple subclasses. The important thing about that concept is that it is defined as a phenomemon or as that which reveals itself. By contrast, we think of moving stars as of today's stars and therefore as noumena. However, on one deeper level, there may be some entities that reveal themselves as today's stars, which would imply the following structure: phenomenon --> phenomenon ... --> noumenon. Of course, one might wonder whether there are any noumena or whether the chain is infinite or even transfinite. For the purpose of today's knowledge, we would not go any deeper, but we must be ready to assume that what appeared to be noumena were in fact phenomena. Which makes noumenon a meta-phenomenon on some level of analysis. Now back to the main subject: it would need to be clarified whether any OR-combination of concepts is considered to be a concept in literature.
Further to be clarified is whether there are adjectival concepts and verbal concepts. Since, instead of saying X is blue, we may say X has-quality blueness, and thus we do not need any concept for adjective "blue". There sure are adjectival and verbal word senses. If concepts are by definition nominal (corresponding to nouns and noun phrases), here would be another difference between concept and word sense.