The 4 main strokes in swimming are the breaststroke, the freestyle or front crawl, the backstroke, and the butterfly. All of these strokes save the butterfly have existed in some form since ancient times. Although there is some debate, the earliest swimming stroke is generally considered to be the breaststroke as it is depicted on cave paintings. However, it is possible that these earlier swimmers were using more of a “doggy paddle” stroke. A variation of the freestyle stroke is depicted on an Egyptian clay tablet and was known to the Ancient Greeks as well. Similarly, a backstroke variation was written about by Plato and others. Swimming has been an important part of health and education throughout many different eras of human history with organized lessons existing throughout Europe. These lessons were about health and water safety and the breaststroke or occasionally a sidestroke variation were taught. While it can be assumed that competitions or informal races were held, they were not codified competition as we understand it today.
As far as modern techniques, they can be traced to the rise of competitive swimming in the late 19th century in Europe (primarily Britain). Early swimming competitions were open water affairs that were concerned with overall distance covered rather than time or speed and swimmers swam a head up version of breaststroke. The British Swimming Federation was founded in 1896 and swimming was included in the first modern Olympic Games. Other national federations were formed over subsequent years culminating with the creation of FINA in 1908. Likewise, different distances for races and eventually different strokes were added as swim competitions became more formalized and swimmers experimented with stroke to increase speed.
The breaststroke was the only stroke in the first swimming competitions. A “frog stroke” was the preferred swimming style throughout much of human history and was characterized by wide arm and leg motions. It was added to the program of the Olympics in the 3rd games in St Louis. By the 1920s the arm motion had been refined to more resemble modern arm movements and the powerful kick associated with the stroke was developed by the 1930s. Due to the inefficiency of the forward arm motion in breaststroke, swimmers experimented with an over water recovery at this time as well and there were two legal versions of the stroke, the classical and the butterfly, until 1953. Subsequent changes to the breathing pattern occurred by the 1960 Olympics that drastically improved times and the 1970s saw further technical improvements. The stroke has also benefited from improvements in the underwater and turning phases in recent years.
The freestyle stroke derived from the transitionary strokes of side stroke and the English stroke that introduced over arm recovery and the scissor kick. Notably, Native Americans competing in England in 1844 used a front crawl type stroke and beat their English opponents; however, this style was looked down upon by the British as unrefined. The stroke was (re-)introduced in competitive swimming in 1873 with the “Trudgeon stroke” which incorporated an over arm pulling motion but was swim head up and with a breaststroke kick. The flutter kick was added by Richard Cavill and he used his technique to great success at the 1902 British International Championship. Hungarians refined the arm stroke to eliminate side-to-side movement and had great success before being replaced by the Australian style that altered the kick to bring the body to a more horizontal position in the water. The technique of freestyle was perfected by Johnny Weissmuller at the 1924 Olympics. Subsequent improvements have been made in arm motions and efficiency, but these are highly technical improvements that don’t really change the “look” of the stroke.
The backstroke was originally done as a double armed stroke with a breaststroke kick. At the Olympics in 1912, Harry Hebner employed an alternating arm stroke and flutter kick to revolutionize the stroke and beat the field. Technical improvements continued to be made throughout the 1920s and 30s, most notably the lifting of the hips from a seated position to the surface of the water. The 1950s saw the introduction of the rolling of the body in the stroke.
As mentioned earlier, the butterfly evolved from the breaststroke and was actually a legal breaststroke variation for a number of years. This stroke was an over arm double recovery as in the butterfly with a breaststroke kick. Prior to being recognized as a separate stroke, many swimmers experimented with a “fishtail” kick, but it was not a legal variant in the breaststroke and resulted in disqualification. The butterfly was officially recognized as a separate stroke with the butterfly kick and separated from breaststroke in 1952.
So, with the exception of the butterfly the swim strokes have existed in some form for most of human history. But it was the rise of competitive swimming that refined the strokes into what we see today. This process was fairly rapid as athletes and coaches experimented with the strokes to find the most efficient technique. This experimentation is an ongoing process and coaches are still making technical adjustments today to gain a competitive edge in races.
This is a subject I know a lot about, but I tried to be succinct here to just address the question as asked. Please feel free to ask for clarification and expansion and I’d be happy to offer it. I can also provide further sources if you are interested.