The national curriculum is taught in Estonian or Russian. In the latter case, Estonian is taught as a first foreign language from the first grade. However, there are schools that use the IB curriculum and teach in English and some private schools that teach in, say, Finnish. The first nine years of education are compulsory, after that one can go to high school, trade school, or work. State schools provide education for free, private schools, naturally, not.
More information here: https://en.wikipedia.org/wiki/Education_in_Estonia.