I can't tell you much about kindergarten. I spent there only one year right before school. Children go there at the age from 2 or 3 to 7 years old. They were organized to be a place were children can stay when their parents are at work, but now they've changed a lot and also give preschool education.
At the age of 7 children go to the Primary school, where they are taught to read, write and count and some times to work with computers. It is just basics of the education. This are classes 1 to 3. Each class is of 25-30 pupils and supervised by one teacher, who also teaching all the lessons. At the age of 10 they go to Middle school which gives basic education on all subjects. This classes numbers are 5 to 9 (class number 4 is skipped now; it was additional class for slow-learners and those who started at 6 instead of 7). There class is also has one teacher, who looks after it, but different classes are teached by different teachers. So at the age of 15 you can leave school and find a work or you can continue to 10th and 11th classes. You can't enter the university with ought them.
If school have a good director who can get mostly good teachers, than school become "elite". It is attended by children from wealthy people and they (rich parents) spend their money to make standard school into good and beautiful. Such was the school my sister transferred and graduated from. Mine school had some good teachers but our late director was a.... can't find polite word to describe her.. So she couldn't keep even what she had in school. I graduated before good teachers left, but my sister transferred on her 6'th or 7'th grade.
We don't have private schools at all. Well, didn't have back when I was at school. Now there are some, they are expensive, but I don't know if they any better. Well, they are new to this, in Soviet Union there was no private organizations of any type.
At the age of 18 you leave the school and considered of age. You can find a work and/or continue to the university.
Our school education too often isn't good enough to enter any of Universities. You have to get some private lessons in the last school year. There are special courses in each University, as well as private courses outside Universities. And you can take private lessons with university teachers. All of this is expensive, but obligatory for entering.
You have to take 3 or 4 exams (depending on university and faculty) if you want to enter payment free course, or just have a "conversation" (don't know right term) with teachers, if you are paying for your studies. And in elite universities you have to take exams even when you are paying. Payment is rather high. It also depends on university and faculty. It is approximately 800$ - 1400$ per semester. My family, for example, won't be able to pay.
In university there are three ways to attend: day, evening and "in absentia" courses. Daily means five years at the univ, 5-6 days a week for first two years, then 3-4 with more focus on self-education. Evening courses are 3 days a week, but for one year longer (6 instead of 5). On "in absentia" courses you study on your own and attend lectures only for a couple of weeks before semester exams.
I'm sorry, I got hit by RL badly. So I'll post what I've finished so far, and continue it in the nest post.