To craft new skills you must first enter Primal World by following the purple quest chain “New Horizons – Summer Reawakened”.
Once you enter Primal World, you must do your Arcane and Mirage Sky quests (from the Sacred Mirror NPC), and level them accordingly.
The books will require you to exchange Old Book Pages for Arcane/Adv. Arcane and Mirage/Adv. Mirage Pages (at the Sacred Cauldron). You also need Primordial Blood.

Sacred Cauldron

Φ True

Ω Dark

Σ Both Esteem

Human

Wu Xia

Fa Shih

Φ | Ω Ferocious Leap Φ | Ω Frozen Flame
Φ | Ω Army Crusher Φ | Ω Armor of Ice
Φ | Ω Repeating Cannon Φ | Ω Frost Blade
Φ | Ω Chasing the Soul Φ | Ω Armor of Earth
Φ | Ω River Avalanche Φ | Ω Sand Fall
Φ | Ω Hillborn Φ | Ω Armor of Fire
Φ | Ω Star Smite
Φ | Ω Dragon Rising

Wingkin

Yu Ling

Yu Mang

Σ Infinite Aura Φ | Ω Kiss of the Snake
Σ Pantheon’s Blessing Φ | Ω Feather Armageddon
Σ Touching the Void Φ | Ω Frost Splash
Φ | Ω Enlightenment Φ | Ω Wing Barrier
Φ | Ω Tornado

Beastkin

Yao Shou

Yao Jing

Φ | Ω Thousand Ton Hammer Φ | Ω Redstone Venomworm
Φ | Ω Bestial Hammer Φ | Ω Grudge Strike
Φ | Ω Defiance Φ | Ω Taboo
Φ | Ω Sundering Heaven Φ | Ω Soul of the Fox
Φ | Ω Tail of the Fox

Tideborne

Xi Shou

Wu Shih

Φ | Ω Elimination Φ | Ω Furious Ocean
Φ | Ω Life Hunter Φ | Ω Glacial Shards
Φ | Ω Benthic Shards Φ | Ω Frost Impact
Φ | Ω Cursed Jail Φ | Ω Shattering Earth Chant
Φ | Ω Sand Flood

Earthen

Jian Ling

Hun Ling

Φ | Ω Dolorous Blow Φ | Ω Azure Mist
Σ Blade of Glass Σ Spore Explosion
Φ | Ω Rockbreaking Blow Φ | Ω Avatar of War Lord
Φ | Ω Chaos Blade Σ Storm Dance
Φ | Ω Windcutting Strike
Φ | Ω Glowing Blade