To work at or make progress through something at a sluggish, strenuous pace, especially for a long period of time. We had to slog through nearly a mile of swamp before we reached solid ground. I've been slogging through this really dense book about economic theory for my college course.
slog through something
to wade or trudge through something, such as mud or snow. Do I have to slog through the snow to go to school? Can't you drive me? When I was your age, I slogged through snow twice this deep to get to school.
To walk or progress through something with a slow heavy pace: The explorers slogged through the swamp. I slogged through both volumes of the author's philosophical writings.