The Swedish school system has remained virtually unchanged since I was born 18 years ago - when it comes to the basics, that is. The actual education, however, and the grade system, has been altered significantly. I will now try to describe to you how the system works - in case you don't care, go read a more interesting node.
Before starting school, it is customary for swedish kids to go to what we call "daghem" (dayhome), "förskola" (pre-school) or "dagis" (daycare). This is the equivalent of kindergarten, and usually contains little or no actual education. Some forms of pre-school include basic maths (count to 1000, add and subtract), reading and writing (the alphabet) as well as physical education. Children usually start pre-school once they're old enough to manage without constant parental attention, and stay in it until school starts.
It should be noted that not all kids start school at age 6 - some start at age 7. To simplify things, this write-up will work on the basis that school starts at age 6. Anyway, the first three years of school are called "lågstadiet" (the low stage), or the 1st, 2nd and 3rd "årskurserna" (grades) - this roughly represents the british primary school. Days are short, lessons are basic and teachers are nice. There are no grades, but kids who do very poorly or exceptionally well will have their parents notified of this fact. At the end of "lågstadiet", kids are expected to know basic maths (without the use of a calculator), be able to read and write proper Swedish and understand basic English, know a bit about the way things work, the world, space and so on. Computers are often used in the education.
This is where students are beginning to actually have their abilites tested beyond the "can do it/can't do it" stage. New subjects, such as "slöjd" (working with wood and cloth, as in carpenting and sewing) are introduced, and days start getting noticeably long. This is also when most kids decide that school is boring, and when the written tests start popping up, it doesn't get any better. These three years - called "mellanstadiet" (the middle stage) or the 4th, 5th and 6th "årskurserna" (grades). Now, students get basic sex ed as well as more science/technology and society-based subjects. Students learn to work in groups and in projects more and more. "Mellanstadiet" is also when students are allowed to customize part of their schedule by choosing from a list of subjects, and start learning one more language - usually French, German or Spanish.
The last bit of "grundskolan" (the basic school), these three years are called "högstadiet" (the high stage) and consist of the 7th, 8th and 9th "årskurs" (grade). Crafts and music get fewer hours now, and eventually disappear completely. PE however remains a constant presense in the curriculum, and continues like that for a few more years. "Högstadiet" introduces even more specialized subjects: Biology, chemistry, religion and even basic economics appear - although usually, the basics of these subjects have already been done in "mellanstadiet". Also, during the 9th grade, the students get to choose one of the most important decisions of their lives: What school to attend next and what kind of education to get there. Of course, to get the education you want you need to have good grades - these are given from 8th grade and onward, in the form of "IG": "icke godkänd" (not approved), "G": "godkänd" (approved), "VG": "väl godkänd" (well approved), and "MVG": "mycket väl godkänd" (very well approved). In "högstadiet", most of the work the students do is done in the style of projects, to prepare for the next stage, where virtually everything is done in projects and groups.
This part of school is actually not compulsory (the first 9 years are), but since most kids have fairly smart parents, and they are not yet old enough to do things like quit school without their parent's consent, the vast majority of all children do go to school for three more years after "grundskolan". This bit, which can actually vary in length between two and 5-6 years, is called "gymnasiet" (the gymnasium). Here, students are divided into "linjer" (lines), "program" (programs) or "utbildningsvägar" (roads of education) - depending on what they want to become in the future. There are lines for aspiring cooks and hockey players as well as wider lines which focus on science, maths or economics and can lead to a large number of different jobs in the future. The most common programs are "naturvetenskapliga programmet" (nature/science program), "samhällsvetenskapliga programmet" (society/science program), "estetiska programmet" (esthetical program) and "internationell ekonomi" (international economy). Host schools also offer localized technology/maths add-ons and special lines directly aimed at certain professions. Here, subjects are replaced by courses - there's not just "Matematik" (Maths) on the schedule - there are the courses "Matematik A" (Maths A), B, C, D and onwards. Each individual student is given a great deal of freedom to choose which courses he wants to go and which he doesn't, however some are compulsory (this varies with each program). All programs usually include some advanced Swedish and English, 2nd language, 3rd language (optional; may be Russian, Latin, etc), semi-advanced maths (derivata, more or less complex equations, matrices, etc), physical education, one or more esthetical subjects (music/singing/arts/acting) and some more or less basic chemistry, religion, economics, politics and so on. Students are usually required to read a lot of books during these three years to expand their knowledge of litterature. The grades achieved during "gymnasiet" are vital when looking for a job, or higher education. "Gymnasiet" lasts for three years, called the 1st, 2nd and 3rd "ring" (rings) or "årskurserna" (grades).
Ages 18 and up
Once the first 12 years of (almost) compulsory school is over, it's the choice of each teenager what he wants to do next. A lot of people go looking for jobs, but to get one on which one can live a good life (depending on your definition of "good", of course) a higher education is a must. Places of higher education in Sweden are called "högskolor" (high schools) or "Universitet" (universities), and they function pretty much like universities do all over the world; nothing particularly weird here. Some of the main universities and "högskolor" in Sweden are "Kungliga Tekniska Högskolan" (the Royal University of Science and Technology) and "Handelshögskolan" (The high school of commmerce". University lasts for 3-5 years.
It is, however, a fact of life in Sweden that every (male) at age 18-19 is required to undergo between 8 and 15 months of military service - hence, the higher education mentioned above is often put off for a year or two while the students learn to wage war. This is obligatory and those who don't want to are summarily thrown in jail for refusing. Naturally, people with handicaps or strange diseases are excepted, and nowadays it is fairly easy to get out of it by simply telling them you don't want to - the Swedish military doesn't get enough money to have every single person in his upper teens do military service. Women don't have to do it in the first place (for some reason) but are allowed to if they want to.
That's all. Swedes reading this, if you feel that you can contribute or correct me, go ahead and do so.