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Lexicography is the study of lexicons, and is divided into two separate academic disciplines. It is the art of compiling dictionaries. 
There is some disagreement on the definition of lexicology, as distinct from lexicography. Some use "lexicology" as a synonym for theoretical lexicography; others use it to mean a branch of linguistics pertaining to the inventory of words in a particular language.
A person devoted to lexicography is called a lexicographer. 
General lexicography focuses on the design, compilation, use and evaluation of general dictionaries, i.e. dictionaries that provide a description of the language in general use. Such a dictionary is usually called a general dictionary or LGP dictionary (Language for General Purpose). Specialized lexicography focuses on the design, compilation, use and evaluation of specialized dictionaries, i.e. dictionaries that are devoted to a (relatively restricted) set of linguistic and factual elements of one or more specialist subject fields, e.g. legal lexicography. Such a dictionary is usually called a specialized dictionary or Language for specific purposes dictionary and following Nielsen 1994, specialized dictionaries are either multi-field, single-field or sub-field dictionaries.
It is now widely accepted that lexicography is a scholarly discipline in its own right and not a sub-branch of applied linguistics, as the chief object of study in lexicography is the dictionary (see e.g. Bergenholtz/Nielsen/Tarp 2009).
Lexicography is the practice of creating books, computer programs, or databases that reflect lexicographical work and are intended for public use. These include dictionaries and thesauri which are widely accessible resources that present various aspects of lexicology, such as spelling, pronunciation, and meaning.
Lexicographers are tasked with defining simple words as well as figuring out how compound or complex words or words with many meanings can be clearly explained. They also make decisions regarding which words should be kept, added, or removed from a dictionary. They are responsible for arranging lexical material (usually alphabetically) to facilitate understanding and navigation. 
Coined in English 1680, the word "lexicography" derives from the Greek λεξικογράφος (lexikographos), "lexicographer",  from λεξικόν (lexicon), neut. of λεξικός lexikos, "of or for words",  from λέξις (lexis), "speech", "word"  (in turn from λέγω (lego), "to say", "to speak"  ) and γράφω (grapho), "to scratch, to inscribe, to write". 
Practical lexicographic work involves several activities, and the compilation of well-crafted dictionaries requires careful consideration of all or some of the following aspects:
One important goal of lexicography is to keep the lexicographic information costs incurred by dictionary users as low as possible. Nielsen (2008) suggests relevant aspects for lexicographers to consider when making dictionaries as they all affect the users' impression and actual use of specific dictionaries.
Theoretical lexicography concerns the same aspects as lexicography, but aims to develop principles that can improve the quality of future dictionaries, for instance in terms of access to data and lexicographic information costs. Several perspectives or branches of such academic dictionary research have been distinguished: 'dictionary criticism' (or evaluating the quality of one or more dictionaries, e.g. by means of reviews (see Nielsen 1999), 'dictionary history' (or tracing the traditions of a type of dictionary or of lexicography in a particular country or language), 'dictionary typology' (or classifying the various genres of reference works, such as dictionary versus encyclopedia, monolingual versus bilingual dictionary, general versus technical or pedagogical dictionary), 'dictionary structure' (or formatting the various ways in which the information is presented in a dictionary), 'dictionary use' (or observing the reference acts and skills of dictionary users), and 'dictionary IT' (or applying computer aids to the process of dictionary compilation).
One important consideration is the status of 'bilingual lexicography', or the compilation and use of the bilingual dictionary in all its aspects (see e.g. Nielsen 1894). In spite of a relatively long history of this type of dictionary, it is often said[ according to whom? ] to be less developed in a number of respects than its unilingual counterpart, especially in cases where one of the languages involved is not a major language. Not all genres of reference works are available in interlingual versions, e.g. LSP, learners' and encyclopedic types, although sometimes these challenges produce new subtypes, e.g. 'semi-bilingual' or 'bilingualised' dictionaries such as Hornby's (Oxford) Advanced Learner's Dictionary English-Chinese, which have been developed by translating existing monolingual dictionaries (see Marello 1998).
A dictionary is a listing of lexemes from the lexicon of one or more specific languages, often arranged alphabetically, which may include information on definitions, usage, etymologies, pronunciations, translation, etc. It is a lexicographical reference that shows inter-relationships among the data.
An encyclopedia or encyclopædia is a reference work or compendium providing summaries of knowledge either general or special to a particular field or discipline. Encyclopedias are divided into articles or entries that are arranged alphabetically by article name or by thematic categories, or else are hyperlinked and searchable. Encyclopedia entries are longer and more detailed than those in most dictionaries. Generally speaking, encyclopedia articles focus on factual information concerning the subject named in the article's title; this is unlike dictionary entries, which focus on linguistic information about words, such as their etymology, meaning, pronunciation, use, and grammatical forms.
A lexicon is the vocabulary of a language or branch of knowledge. In linguistics, a lexicon is a language's inventory of lexemes. The word lexicon derives from Greek word λεξικόν, neuter of λεξικός meaning 'of or for words'.
Lexicology is the branch of linguistics that analyzes the lexicon of a specific language. A word is the smallest meaningful unit of a language that can stand on its own, and is made up of small components called morphemes and even smaller elements known as phonemes, or distinguishing sounds. Lexicology examines every feature of a word – including formation, spelling, origin, usage, and definition.
Sandro Nielsen is a Danish metalexicographer, Associate Professor at Centre for Lexicography at the Aarhus School of Business, Denmark, from where he received his PhD in 1992. Nielsen has contributed to lexicography as a theoretical and practical lexicographer with particular reference to bilingual and multilingual specialised dictionaries. He is the author and co-author of more than one hundred publications on lexicography, theoretical papers, printed and electronic (online) dictionaries.
Legal lexicography is the complex of activities concerned with the development of theories and principles for the design, compilation, use, and evaluation of dictionaries within the field of law, see e.g. Nielsen 1994.
A language-for-specific-purposes dictionary is a reference work which defines the specialised vocabulary used by experts within a particular field, for example, architecture. The discipline that deals with these dictionaries is specialised lexicography. Medical dictionaries are well-known examples of the type.
A specialized dictionary is a dictionary that covers a relatively restricted set of phenomena. The definitive book on the subject includes chapters on some of the dictionaries included below:
A law dictionary is a dictionary that is designed and compiled to give information about terms used in the field of law.
Specialized lexicography is an academic discipline that is concerned with development of theories and principles for the design, compilation, use and evaluation of specialized dictionaries. A specialized dictionary is a dictionary that covers a relatively restricted set of phenomena, usually within one or more subject fields. An alternative term for this type of dictionary is LSP dictionary.
A Greek–English Lexicon, often referred to as Liddell & Scott or Liddell–Scott–Jones (LSJ), is a standard lexicographical work of the Ancient Greek language originally edited by Henry George Liddell, Robert Scott, Henry Stuart Jones, and Roderick McKenzie and published in 1843 by the Oxford University Press.
Centre for Lexicography is a research centre affiliated with the Aarhus School of Business, University of Aarhus Denmark, and was established in 1996. The centre's aim is to carry out lexicographic research into needs-adapted information and data access, i.e. research work into dictionary theory in general and it has built a solid, international reputation in that field.
An electronic dictionary is a dictionary whose data exists in digital form and can be accessed through a number of different media. Electronic dictionaries can be found in several forms, including software installed on tablet or desktop computers, mobile apps, web applications, and as a built-in function of E-readers. They may be free or require payment.
A bilingual dictionary or translation dictionary is a specialized dictionary used to translate words or phrases from one language to another. Bilingual dictionaries can be unidirectional, meaning that they list the meanings of words of one language in another, or can be bidirectional, allowing translation to and from both languages. Bidirectional bilingual dictionaries usually consist of two sections, each listing words and phrases of one language alphabetically along with their translation. In addition to the translation, a bilingual dictionary usually indicates the part of speech, gender, verb type, declension model and other grammatical clues to help a non-native speaker use the word. Other features sometimes present in bilingual dictionaries are lists of phrases, usage and style guides, verb tables, maps and grammar references. In contrast to the bilingual dictionary, a monolingual dictionary defines words and phrases instead of translating them.
Beryl T. "Sue" Atkins was a British lexicographer, specialising in computational lexicography, who pioneered the creation of bilingual dictionaries from corpus data.
Computational lexicology is a branch of computational linguistics, which is concerned with the use of computers in the study of lexicon. It has been more narrowly described by some scholars as the use of computers in the study of machine-readable dictionaries. It is distinguished from computational lexicography, which more properly would be the use of computers in the construction of dictionaries, though some researchers have used computational lexicography as synonymous.
In digital lexicography, natural language processing, and digital humanities, a lexical resource is a language resource consisting of data regarding the lexemes of the lexicon of one or more languages e.g., in the form of a database.
Ultralingua is a single-click and drag-and-drop multilingual translation dictionary, thesaurus, and language reference utility. The full suite of Ultralingua language tools is available free online without the need for download and installation. As well as its online products, the developer offers premium downloadable language software with extended features and content for Macintosh and Windows computer platforms, smartphones, and other hand held devices.
Tom McArthur was a Scottish linguist, lexicographer, and the founding editor of English Today. Among the many books he wrote and edited, he is best known for the Longman Lexicon of Contemporary English, the first thematic monolingual learner's dictionary, which complemented the Longman Dictionary of Contemporary English by bringing together sets of words with related meanings, Worlds of Reference, as well as the Oxford Guide to World English.