Common skill books (Military/Development/Subordinate City) ranked F2P sources: Relics - collect 25 fragments for a chance at a Lv4/Lv3 skillbook or a Skill Book Page (best way to get a Lv4 book without paying); Gather Troops event - completing quotas gives a Luxury Treasure Chest per tier, each always containing 1 Skill Book Page (10 pages = 1 Lv4 book), daily players get 10+ chests; Viking Challenge event - Easy 50 Vikings gives Lv3 x1, Normal 50 gives Lv3 x2, Hard 50 gives Lv4 x1 (needs ~100,000 tier-10 cavalry); disassembling unwanted skillbooks gives 1/2/3/4 pages for Lv1/2/3/4 respectively (10 pages = 1 Lv4 book); Wheel of Fortune in Tavern can randomly give a Lv1 book or Skill Book Chest; Academy Skill Books Shop sells only low-level books for gems (Lv1 3,000g, Lv2 5,000g, Lv3 8,000g). Debuff skill books mainly come from the Bacchus Tavern gacha event (collect Bacchus Gold Coins, redeem a Debuff Skill Book Chest for a random Lv1-4) or a $99.99 paid package. Duty skill books: Academy shop sells Lv1 only, limited to a specific building list, for 3,000 gems, or $99.99 paid packages for Lv1-4.
Original research source: Evony Guide Wiki