Ok so basically, a really really long time ago an event happened called "the conjunction of the spheres" where the multiverses converged into one, the "human" world was destroyed and so they inhabited the new world mixed with elves and monsters, the humans eventually learned magic and took over the new world and just overwhelmed the elves to the point where humans took over. Some races of elves kind of hate humans for this still even though it happened thousands of years ago.

Fast forward and humans are tired of monsters so they begin to hire people to hunt them down, these people are called witchers and are trained from childhood to track and kill monsters. They go through a process called the "trial of the grasses" in which they ingest mutagens to increase physical strength, speed and awareness. It was during this process that Geralt was discovered to be able to withstand more mutations than the others and he underwent extra training and experiments, making him immune to disease and resistant to pain and he's just overpowered basically.

There's this thing called the "law of surprise", which is where a witcher can request payment. It states that a witcher can request the first thing a contract giver sees when they return home, this is how Geralt came to be the adoptive father of Cirilla Fiona Elen Riannon, daughter of Pavetta and the emperor of Nilfgaard; Emhyr var Emreis. Girls can't be witchers obviously since they're only good in the kitchen or as sorceresses, so she underwent witcher training but isn't technically a witcher as she hasn't undergone the trial of the grasses. Ciri grew up and seemingly vanished from the face of the earth.

Geralt x Yennefer is the true ship, one of the first short stories in the covers how they met, Geralt captured a djin alongside his bestie Dandelion and was granted three wishes, the last of which was to never be separated with the powerful sorceress Yen who he had just met but she fine so it's all good. Since then fate keeps bringing them together.

Some more about Dandelion, he's a bard, poet and something of a ladies man, Geralt helped him escape the brothers of some woman he had sex with. Its covered in the first book which is only a couple of short stories and I definitely recommend it.

Another love interest for Geralt is the sorceress Triss Merigold. Geralt lost his memory during a battle before the first game and was helped back to health by her. She developed feelings for him and in his amnesiac state he developed feelings for her too. Yen and Triss are both in the Lodge of Sorceresses and are considered friends which is kind of awkward since they both know about the love triangle.

On top of all this there's also a huge war going on for control of the continent, the Nilfgaardian empire to the south controlled by emperor Emyhr seem like bad guys at first but they also bring law, order and high society culture despite being harsh and cruel. Meanwhile the northern kingdom of Redania has been expanding under the rule of King Radovid V, a crazy paranoid king who persecutes magic users and murders people in cold blood for even thinking about disagreeing with him. There's no real good guys side to the conflict, which is fair enough since Geralt canonically tries to stay impartial in all matters.