Hardwood is a good choice for flooring for on-grade or above-grade concrete floors. On below-grade concrete floors, engineered hardwood flooring is a better choice. In either case, the concrete floor must be absolutely dry and a vapour barrier installed to keep it that way, or the new flooring will buckle. Preparing the concrete floor properly is crucial to getting a desirable result.
The short answer to the question "Can you install hardwood over uneven concrete?" is no. Hardwood is a highly malleable material. If the concrete floor is uneven, the flooring will warp, buckle and expand in weird ways. But all is not lost --- you can fix the problem.
Testing for Evenness
The first thing to do is to find out if the concrete floor is uneven. Place a 6-foot- to 10-foot-long straightedge on the floor. If the concrete does not meet the straightedge at every point, the floor is uneven. Repeat this test over and over until you believe that you have pretty much covered the entire floor. The concrete could be even in one quadrant, but not in another. Note that placing a 2-foot-long carpenter's level at various spots will not give you the information you need. The level is too short.
Levelling the Floor
The problem of an uneven concrete floor can be solved by applying a self-levelling concrete overlay to the floor. This is a major undertaking. First, the floor must be thoroughly cleaned to get rid of grease, oil and grime that could prevent the self-levelling concrete overlay from adhering. Hopefully, this step will require only a liquid cleaner, but if the concrete floor is very dirty, getting it clean could require utilising a mechanical process. Then the floor must be primed and the primer allowed to dry to a tacky film. Mix the self-levelling overlay according to the manufacturer's directions and pour it on the floor. Smooth the material with a steel spreader to allow it to flow easily over the floor and fill in the depressions. Make sure to allow the self-levelling concrete to dry and cure according to the manufacturer's instructions.
Laying the Hardwood Flooring
From this point on, lay the hardwood flooring just as you would in any other circumstance. Install a vapour barrier on top of the slab so that moisture cannot migrate from the concrete floor into the hardwood flooring. The vapour barrier could be two layers of asphalt felt applied with an asphalt mastic or 6-mil polyethelene sheeting. Next comes the subfloor, which could be 3/4-inch treated plywood affixed with concrete screws every 16 inches. A gap of 3/4 inches along the walls and a gap of about 3/8 inch between the sheets of plywood allow the concrete to expand. Finally, nail the hardwood floor to the subfloor using a floor nailer. Then sand and coat the hardwood flooring with at least three coats of polyurethane.