Linguistic Typology

Linguistic Typology is the analysis, comparison, and classification of languages according to their common structural features and forms. This is also called cross-linguistic typology. 

"The branch of linguistics that "studies the structural similarities between languages, regardless of their history, as part of an attempt to establish a satisfactory classification, or typology, of languages" is known as typological linguistics (Dictionary of Linguistics and Phonetics, 2008).

Examples 

"Typology is the study of linguistic systems and recurring patterns of linguistic systems. Universals are typological generalizations based on these recurring patterns.
"Linguistic typology took off in its modern form with the ground-breaking research of Joseph Greenberg, such as, for example, his seminal paper on a cross-linguistic survey of word order leading to a series of implicational universals (Greenberg 1963). . . . Greenberg also attempted to establish methods for quantifying typological studies, in order that linguistic typology could meet scientific standards (cf. Greenberg 1960 [1954]). Furthermore, Greenberg re-introduced the importance of studying the ways languages change, but with the emphasis that language changes give us possible explanations for language universals (cf., for example, Greenberg 1978).
"Since Greenberg's pioneering efforts linguistic typology has grown exponentially and is, as any science, continuously being enhanced and redefined as to methods and approaches. The last few decades have seen the compilation of large-scale databases with the help of ever more refined technology, which have led to new insights as well as given rise to new methodological issues."
(Viveka Velupillai, An Introduction to Linguistic Typology. John Benjamins, 2013)

Tasks of Linguistic Typology

"Among the tasks of general linguistic typology we include . . . a) the classification of languages, i.e., the construction of a system to order natural languages on the basis of their overall similarity; b) the discovery of the mechanism of construction of languages, i.e., the construction of a system of relationships, a 'network' by means of which not only the obvious, categorial mechanisms of language can be read but also the latent ones."
(G. Altmann and W. Lehfeldt, Allgemeinge Sprachtypologie: Prinzipien und Messverfahren, 1973; quoted by Paolo Ramat in Linguistic Typology. Walter de Gruyter, 1987)

Fruitful Typological Classifications: Word Order

"In principle, we might pick on any structural feature and use it as the basis of classification. For example, we could divide languages into those in which the word for a canine animal is [dog] and those in which it isn't. (The first group here would contain exactly two known languages: English and the Australian language Mbabaram.) But such a classification would be pointless since it wouldn't lead anywhere.
"The only typological classifications which are of interest are those which are fruitful. By this, we mean that the languages in each category should turn out to have other features in common, features which are not used to set up the classification in the first place.
"[The most celebrated and fruitful of all typological classifications has proved to be one in terms of basic word order. Proposed by Joseph Greenberg in 1963 and more recently developed by John Hawkins and others, word-order typology has revealed a number of striking and previously unsuspected correlations. For example, a language with SOV [Subject, Object, Verb] order is highly likely to have modifiers that precede their head nouns, auxiliaries that follow their main verbs, postpositions instead of prepositions, and a rich case system for nouns. A VSO [Verb, Subject, Object] language, in contrast, usually has modifiers that follow their nouns, auxiliaries that precede their verbs, prepositions, and no cases."
(R.L. Trask, Language, and Linguistics: The Key Concepts, 2nd ed., edited by Peter Stockwell. Routledge, 2007)

Typology and Universals

"[T]ypology and universals research are intimately related: if we have a set of significant parameters whose values none the less show a high degree of correlation, then the network of relations among these parameter values can equally be expressed in the form of a network of implicational universals (absolute or tendencies).
"Clearly, the more widespread the net of logically independent parameters that can be linked in this way, the more significant is the typological base being used."
(Bernard Comrie, Language Universals, and Linguistic Typology: Syntax and Morphology, 2nd ed. The University of Chicago Press, 1989)

Typology and Dialectology

"There is evidence from linguistic varieties around the world, including Greek dialects, to suggest that the distribution of structural characteristics over the world's languages may not be entirely random from a sociolinguistic point of view. For example, we have seen indications that long-term contact involving child bi-lingualism may lead to increased complexity, including redundancy. Conversely, contact involving adult second language acquisition may lead to increased simplification. Furthermore, communities with dense, tightly-knit social networks may be more likely to demonstrate fast-speech phenomena and the consequences of this, and more likely to experience unusual sound changes. I would like to suggest, moreover, that insights of this type can complement research in linguistic typology by giving an explanatory edge to the findings of this discipline. And I would also suggest that these insights should give some sense of urgency to typological research: if it is true that certain types of linguistic structure are to be found more frequently, or possibly only, in dialects spoken in smaller and more isolated communities, then we had better research these types of communities as rapidly as we can while they still exist."

Source

Peter Trudgill, "The Impact of Language Contact and Social Structure." Dialectology Meets Typology: Dialect Grammar From a Cross-linguistic Perspective, ed. by Bernd Kortmann. Walter de Gruyter, 2004