The Sunspot cycle was first discovered by Samual Heinrich Schwabe, who, in 1943, completed his 15 year research into mysterious dots that have been appearing on the Sun. These dots were once thought of as undiscovered planets within the orbit of Mercury, most famous of which was the hypothesised Vulcan planet. The search for the hypothesised planet began in the early 1800s when it was observed by Urbian Jean Joseph Leverrier, during modelling of Mercury's orbital behavior based on Sir Isaac Newton Laws of Motion, that Mercury experienced anomalies in its orbit, which led to the conclusion that there must be another planet orbiting closer to the Sun than Mercury.
The search for this missing planet began and lasted for decades, finally being laid to rest when Mercury's unusual orbit was explained by Albert Einstein's Theory of Relativity. Schwabe began his research for the missing planet in the 1830s. His findings did not lead to the discovery of a new planet; instead, he noted that every 11 years, what we now know as Sunspots go through a cycle where their numbers increase to form large groups of spots and the spots themselves increase in size, then decrease in number and size.
The Sunspot cycle lasts for about 11 years, and is part of a larger solar cycle that lasts 22 years and is a result of the complexities of the Sun's magnetic field, cause by the differential rotation of the Sun, and of the motions of the underlying convection zone. The 11 year figure is an average however, as since 1700 cycles have been observed to have a duration of anywhere between 9 years and 14 years. The sunspot cycle is part of a larger and longer solar event known as the solar cycle, known to last for up to 22 with different solar activities such as solar flares and increased velocity of the solar wind. At the end of every sunspot cycle, the magnetic poles of the Sun reverse from North-South to South-North; at the end of the entire solar cycle, the magnetic poles return to their original North-South position.
As previously mentioned, during any one cycle there is a huge variance in the number of spots present at different times. The maximum number of sunspots occurs during what is known as solar maximium; the least number of sunspots occur during what is known as solar minimum. The number of sunspots that have occurred during each cycle have varied tremendously, and no one knows why there is such a variance of sunspot numbers between each cycle. The number of sunspots that occur during every cycle is now measurable, however, by using the Wolf sunspot number, which is a formula developed by Rudolf Wolf, a Swiss astronomer, in 1848. The duration of each individual spot also varies widely: some lasting a few hours, and some can go on for a few months.