Cookware is anything you cook in, whether in the oven, on top of the stove, over a campfire or in a microwave. At a minimum, such items need to be heat resistant. For stove-top use, they need to be flame-resistant as well. For microwave use, they need to be microwave safe.
Various materials can be used to make cookware out of. Each type of material has different uses, different strengths and different weaknesses.
Materials used include aluminum, cast iron, copper, non-stick, or porcelain on carbon steel, porcelain-coated, stainless steel, tempered glass and pottery.
Different shapes are designed for different tasks.
Wood handles stay cool, but don’t fare well in the oven or dishwasher.
The best handles are those riveted on.
You can buy cookware in sets, or open-stock. Most people advise to start off with a set, to get the most bang for your buck, and then add on to it through open stock.
Sources
Blumenthal, Dale. Is That Newfangled Cookware Safe? US Food and Drug Administration. FDA Consumer Magazine. October 1990.