From Wikipedia, we are given this definition of “horology.”

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“Horology (via Latin horologium from Greek ὡρολόγιον, from ὥρα hṓra “hour; time” and -o- interfix and suffix -logy; lit. “the study of time”) is the art or science of measuring time. Clocks, watches, clockwork, sundials, hourglasses, clepsydras, timers, time recorders, marine chronometers, and atomic clocks are all examples of instruments used to measure time. In current usage, horology refers mainly to the study of mechanical time-keeping devices, while chronometry more broadly includes electronic devices that have largely supplanted mechanical clocks for the best accuracy and precision in time-keeping.
People interested in horology are called horologists. That term is used both by people who deal professionally with timekeeping apparatus (watchmakers, clockmakers), as well as aficionados and scholars of horology. Horology and horologists have numerous organizations, both professional associations and more scholarly societies.”
Did you know there are entire websites dedicated to Horology? “During the first public surge of interest in the internet in the mid-1990’s, Fortunat Mueller-Maerki, a longtime member of the NAWCC (National Association of Watch and Clock Collectors), created Horology – The Index at http://www.horology.org as part of the WWW-Virtual Library; probably the most comprehensive, hierarchical, not-for-profit collection of virtual information resource links in existence at that time. That index page and its subsidiary pages attempted to provide a comprehensive index of active links and cross-links to as much horological information on the WWW as could then be found….In 2005, Ted Orban developed The Horology Source to provide to the global horological community an expanded and updated resource of horology links. Over the years, The Horology Source grew to encompass more than 5,700 active links.The NAWCC Internet Advisory Committee in 2009 spearheaded th e process to implement Horology – The Index in the NAWCC space. Ted Orban agreed to design the site and infrastructure, transfer the content from The Horology Source, and maintain the site going forward. Now, the new Horology – The Index at NAWCC combines the best of these two great horological resources.”
There are several institutions/associations that devote their efforts to Horology, including the British Horological Institute, which produces a Horological Journal. “The British Horological Institute is a professional body created by the members, for the members, to further their interests. We aspire to be the natural home for all involved in horology, whether professionally or recreationally, and we will achieve this by:
Facilitating education and providing specialist training;
Setting recognised standards of excellence in workmanship and professional conduct;
Supporting our members in the furtherance of their horological aspirations.
Membership of the BHI is open to anyone from any part of the world. Professional membership grades are ‘Member’ and ‘Fellow’ – these are recognised professional qualifications. ‘Associate’ level is open to non-qualified people who have an interest in timekeeping.”
Birmingham City University has an BA(Hons) course in Horology. “This course is the only one of its kind, designed to train and create employable students in horology, tailored to meet the growing global demand for watchmakers and clockmakers, qualified to the industry standard.”