Maille is the period-correct French term for what has commonly been called "chainmail" since Victorian times and now modernly in D&D. 'Mail' is the English term. Maille is made of many interlocking metal rings, and one of the most common forms of armour was the maille hauberk.
In Europe, the 1-to-4 pattern was completely dominant. In East Asia (primarily Japan), mail was also common, but here several more patterns were utilized and an entire nomenclature developed around them. In the Middle East and India, yet other patterns were developed (but 1-to-4 being the most common) and often combined with metal plates linked in with the rings.
Historically, the rings composing mail armour would be riveted or welded shut, to reduce the chance of the rings splitting open when subjected to a thrusting attack or a hit by an arrow. Also structural integrity of the garment could be held without a heavier gauge of wire, when compared to butted mail.
In modern re-enactment and live-action roleplaying games, split sprung steel washers are sometimes used. Usually a two pairs of pliers are used to bend the washers open and closed whilst "knitting" the chainmail. The resulting mail is usually heavier than traditional wire-wound mail, which is also used by reenacment groups.
Members of the New Varangian Guard and other Australian reenactment groups sometimes make their maille from spring steel rings. By using spring steel, you can use a finer gauge of wire and still retain strength. However, for truly tough and light maille, you cannot go past riveted maille. Another option, if you have the money, is always titanium - strong, light and if you ask some nicely they might anodize it for you.
In the SCA, you will find people whose skill at making historically accurate mail varies right across the spectrum; from amateur to true artisan.