Three methods of extending your network coverage without extra wires are mesh and wireless extenders and power-line adaptors.
All extend the network in the same way, they both create an additional access point at a different location to your router. As an example, in a three-story house you could have your router on the ground floor and an extender/adaptor on the first floor, this would mean that no part of the house is more than one floor away from an access point.
Out of the three, mesh networking is the best performing option. The mesh hardware usually comes in packs of three allowing you to add more mesh points if required.
Each mesh point can talk to each other so instead of a traditional wireless extender talking to a main base station, each mesh node can talk to another mesh node until the data gets back to the central node.
This can also adapt automatically to the environment so if you move things around and another mesh node can be seen with a better signal, it will automatically route this way.
The advantage of having a wireless extender is that it's truly wireless, there's no need for any wires. The only thing you will require is a plug socket for the adapter.
The disadvantage of a wireless extender is that it relies on the existing wireless signal, so you would need to place it so that it has a good wireless connection with your router.
The advantage of powerline adapters is that it doesn't rely on wireless signal, so you could place it in an optimal position to maximise the effect of the rebroadcasted wireless signal.
The disadvantage of powerline adapters is that it relies on your existing wiring within the property and that the two plug sockets that the adapters plug into are on the same circuit.
The best solution would depend on many things, including the building and where the original access point is located, which means different solutions will be more beneficial in different situations.