Fresh cheese is not aged before eating. These cheeses are soft and generally mild, sometimes slightly tart, and taste like the milk they are made from. Since they are young, they have no rind and often don't even hold their shape. Examples are fresh chèvre, Mexican queso fresco, cottage cheese, farmer's cheese, mascarpone, paneer, manouri, quark, and ricotta. Some types are sold both fresh and aged: pizza mozzarella is the aged version of fresh mozzarella balls.
These cheeses have a characteristic "bloomy" crust, created when bacteria ripen the cheese from the inside out. They are usually disc-shaped to provide lots of surface area for the bacteria to develop. As they ripen, a delicious soft- to near-liquid layer forms below the rind. Cheeses range from mild and buttery to strong. Usually eaten at three to eight weeks old, examples include Brie and Camembert.
Semi-Soft to Semi-Hard Cheese
A great range of cheeses fall into this category. These might be young versions of cheeses that age well--like Cheddars--or creamy monastery-style cheeses. Washed-rind cheeses--or cheeses that have been washed with brandy, wine, or a brine during ripening--also fall in this category and can be semi-soft like Italian taleggio, to fairly firm, like Spanish Mahon.
Semi-hard to Hard Cheese
These are older, drier, and often saltier, with bolder flavors. Often tiny, salty protein crystals develop in them as they age, giving a distinctive texture. Aged Cheddar, Gruyere, Dry Jack, and Parmigiano Reggiano, fall into this category.