Robert Moog is considered the father of analog synthesizers

The first Moog modular prototype was built in in 1964, with orders for custom systems being taken as early as 1965, and a commercially available product line by 1967. His synthesizers gave way to the modern ones we have today.
Here is the first synthesizer that he released in 1967-
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"As imposing as these systems may look, they are merely solid walnut cabinets housing smaller dedicated function “modules” which, when interconnected by patch cables, can be used to create, shape and manipulate electronic sounds into musical bliss."
Moog explains his synthesizer-

He says that his synthesizers are a collection of modules, including a few oscillators, a couple envelopes, and amplifiers. Basically a typical synthesizer, he was just the inventor of the first modern one.
The first ones were 6 or 7 feet high, but in the video above, he demonstrates the Mini-Moog, which is obviously much smaller. Now a days, synthesizers can be as thin as regular electronic piano.
The biggest difference is, back in 1967, Moog's modules were very straightforward, while today they have become increasingly complicated on some, as to create more complicated sounds.

When they were new, Moog modular synthesizers were very expensive. They originally sold between $2,000 and $10,000 for complete systems; individual modules varied from $100 to $1,300 each.