There are four mainline games in the Batman: Arkham series: Batman: Arkham Asylum, Batman: Arkham City, Batman: Arkham Origins, and Batman: Arkham Knight.
Arkham Asylum began the series in 2009, placing Batman inside the heavily fortified psychiatric facility after the Joker seizes control. Arkham City followed in 2011, expanding the setting into a prison district built within Gotham. Arkham Origins, released in 2013, is a prequel developed by WB Games Montréal and follows a younger Batman early in his career. Arkham Knight arrived in 2015 as Rocksteady’s concluding main installment and introduced the Batmobile as a major gameplay feature.
The count is sometimes confused because the wider Arkham franchise includes spin-offs such as Arkham Origins Blackgate, Arkham VR, Arkham Shadow, mobile games, and Suicide Squad: Kill the Justice League. Those titles belong to the broader Arkham-related continuity, but the traditional mainline count remains four.