Riai refers to the mutual principles of movement found in Traditional Aikido training. O-Sensei created a trinity of Tai-jutsu (the empty-handed techniques of Aikido), Aiki-ken (sword) and Aiki-jo (staff). The sword (in practice, the Bokken or wooden sword) and Jo (staff) are both traditional weapons in Japanese Budo. But O-Sensei developed the use of these two weapons into something very much his own.
The body movements, hip movements, hand movements and evasive positioning are all connected to each other, whether using one of these weapons or not.
Practicing Aiki-ken and Aiki-jo is not only a very interesting and fascinating type of training in itself, but it enhances every aspect of the body techniques as well. Learning these universally applicable principles enables the Aikido practitioner to handle attacks from multiple opponents, as well. This is due to the principle of moving off the line of attack in the initial defensive movement; something that is very easily understood when practicing against an attacker with a sword or staff!