THE PRIMARY goal of Islam, according to its doctrine, is to bring the law of Allah (known as Sharia) to all people on earth. That isn't much different than similar goals of other religions. The thing that makes Islam different is the methods their doctrine allows them to use.
Islam's doctrine is unique because its history is unique. The three other large, fairly recent religions (Buddhism, Christianity, and Taoism) arose within an already-existing legal system. The methods they could use to spread their religion were limited by that system. Christianity, for example, arose at a time when Judaism was strong, and Rome was even stronger. If Christians had been armed insurrectionists, if they had tried to take over the Roman government, if they had tried gaining converts by force, Christianity would have been annihilated before it really got started.
The same can be said for Buddhism and Taoism.
The same was also true for Islam when it first started in Mecca. Mohammad and his followers were a minority and had to practice tolerance of others (or be crushed). But when they moved to a new city (Medina), things changed. They soon ruled that city. In Arabia at the time, no overriding legal or military power existed — the region now known as Saudi Arabia was made up of independent tribes and clans.
In other words, the religion of Islam arose where there was no external imposition of limits, and it developed a religious doctrine quite different from other religions we are familiar with. Islamic doctrines unapologetically advocate the use of force, warfare, deceit, fear, torture, and slaughter to bring the law of Allah to the world. This sounds really horrible, but I'm not making this up. You can verify this all yourself, and I wish you would. You should start by reading the Quran. It has been made relatively easy for you.
In their time, nothing existed to stop the fledgling religion from employing any means necessary. Unfortunately, it was all written down and has been considered holy doctrine ever since.
Since Mohammad existed in the seventh century, his biographical details were also written down and were never lost. What he did and said is well-preserved, as is the unaltered, unedited holy book of Islam, the Quran.
Unfortunately for non-Muslims, it says in the Quran no less than 91 times that a Muslim should follow Mohammad's example in all things and for all time.
So Islam's prime directive is to bring the law of Allah to all people on earth using any means necessary. You can say Islam's mission in three words: Islam must dominate. That's the bad news for us non-Muslims. The good news is that many people who consider themselves Muslims don't know much about Islam, and even some who know about this prime directive are not interested in pursuing it.
Some are pursuing it earnestly, however, and it is worth knowing about because some of the ways they're pursuing it are pretty clever. Learn more about that here: Perfectly Legal Jihad. Once you know what's going on and what devout, orthodox Muslims are aiming at, it is a lot easier to prevent them from gaining any ground.