Not free, but in addition to AoPS.com books and website, I highly recommend : - Algebra book by Gelfand [ amazon print n demand I guess ] - A Decade of the Be

Not free, but in addition to AoPS.com books and website, I highly recommend : - Algebra book by Gelfand [ amazon print n demand I guess ] - A Decade of the Berkeley Math Circle by Zvezdelina Stankova and Tom Rike - The Art and Craft of Problem Solving by Paul Zeitz Also have a look at https://mathcircles.org https://mathcircles.org and any math competitions available locally