The epidermis is composed primarily of what kind of tissue?
First, it's important to recognize some subtle nuances in scientific vocabulary. It's fairly common for a word to refer to two completely separate things; in this case, "epidermis" can refer to the outer of layer of an animal, and it can also refer to the outer layer of a plant. I'm going to assume that we're talking about animals, since most biology classes focus on them, but we should always be very clear about what we're referring to so that we avoid giving dubious answers.
Second, we should define what a "tissue" is. In any animal there are several levels of organization; we might say that the animal can be organized according to separation of tasks attributed to certain organs, or that the cells themselves are different based on their functions. Indeed, we know that a nerve cell is very different from a blood cell in form and function. Tissues are a sort of intermediate level of organization, halfway between a cell and an organ. A tissue is a group of similar cells that have banded together to work toward a common purpose.
In animals, there are four general categories of tissue: muscle, nervous, connective, and epithelial. The skin is considered to be made up of epithelial tissue.
While there are different layers of the skin, and each layer may have a slightly different composition of cells, all of those cells will be classified as epithelial tissue, because they all perform a common function; insulating the body from the environment. While the cells themselves may vary considerably, any epithelial cell will still be better at protecting the body from the environment than, say, a nervous cell.