"Battletech" is a game where giant robots slug it out on a futuristic battlefield among infantry, tanks, helicopters, fighters, and everything in between. If that alone doesn't sound interesting, I don't know how to help you. "Battletec"h was launched in 1984 and has since become a very popular tabletop game and all-encompassing mecha franchise. Although "Battletech" took a small hiatus due to image copyright violations, it came back in full force in the late 2000s.
The game plays similarly to most other tabletop games. Players roll for initiative each turn, then movement and combat takes place and damage is doled out. It's important to note that the winner for initiative actually goes second – the theory behind this rule is that reacting to your opponents movements is more potent than acting first.
"Battletech" can be played on a hexagonal map system or on open terrain, but regardless, movement and actions play a more critical role than other tabletop games. While other wargames give units a maximum move distance, usually without penalties, players need to think very carefully about how their mechs move. Each movement and action generates a certain amount of heat depending on what was performed, and overheating has drastic consequences. More strenuous types of movement like jumping come with higher heat costs and the same goes for firing different types of weapons. Although it might sound frustrating to limit movement and firing, it creates tactical depth.
Damage is delegated on specific locations to a unit's body. Each unit has a different accompanying chart which adds another tactical layer to the game over the typical health/hull point limit. Although some weapons can't usually damage higher armor values, Battletech uses a floating critical system which allows some of the smallest of arms to put a dent in larger targets. It may be frustrating to take a hit from something that normally wouldn't damage your giant mech, but this only happens on rare occasions and gives weaker units a slight chance to stand against the big guns.
"Battletech" takes place in the 31st century where humanity emerges from a golden age of unity with guns blazing. Technology lost during that time of peace is being rediscovered which gave rise to the dominance of mechs on the battlefield. There are numerous factions at play spread out among the stars. Although the "Battletech" universe uses many sci-fi tropes like nanotechnology, aliens are nonexistent except for a few minor encounters in some of the books.
Essentially, an inner governing force called the Star League ruled over most of humanity but experienced enough inner turmoil to throw things out of order. After some infighting and reestablishing, a group of radicals that had fled known space returned to wage war. The Star League won out, but humanity once again collapsed in on itself and every single house, faction, and government fought each other and themselves.
Where to find it:
Given its popularity and longevity, "Battletech" tends to be more prevalent in tabletop stores than other wargames. There's no guarantee that your local brick and mortar houses any of their products, however, and so your best bet is to scour online retailers for their minis. If you don't feel confident enough to spend money on the rulebook just to see if you want to play the game, check out the quickstart rules in this free online PDF.