5E Spell Groupings by Tradition

Most spells in the 5th Edition Player's Handbook fit snugly within one of four dominant magical traditions on Taharjin's Flame, although certain spells have been omitted because of a lack of matching concepts in this world, particularly Planar magic. But, good news! Because there are no Clerics in TF, many spells from this class list have been retooled for wizardly use. Hooray! Where this happens, the qualifier "Divine" should be ignored: only the effect of the spell is relevant.
The list below should be seen as exemplary rather than definitive. Original creations are in process, and will be added as they spindle out of either my brain, or the ones in my players' skulls.

All Traditions

Mages from all Traditions can cast the Level 1 spell, Detect Magic, at will.

Berythian

As per the The Model of the Elements, the Four elemental Forces are ordered in The Berythian Tradition according to their universal procession: first, Fire, represented by the dragon Taharjin; Earth, represented by Eadthuum, a titan; Water, represented by Haldorm, a whale; and Air, represented by a mythic bird, the Daovbehna.

TAHARJIN (FIRE)

Cantrip: Fire Bolt, Light, Prestidigitation (cannot create illusory object), Produce Flame, Sacred Flame, Searing Smite, Thaumaturgy
Lvl 1: Burning Hands, Chromatic Orb, Faerie Fire, Guiding Bolt, Hellish Rebuke, Identify, Mage Armor, Magic Missile, Unseen Servant,
Lvl 2: Arcane Lock, Blindness/Deafness (only Blindness), Branding Smite, Continual Flame, Darkvision, Flame Blade, Flaming Sphere, Heat Metal, Magic Weapon, Scorching Ray
Lvl 3: Blinding Smite, Daylight, Elemental Weapon, Fireball, Glyph of Warding
Lvl 4: Conjure Minor Elementals, Fabricate, Fire Shield, Wall of Fire
Lvl 5: Contact Other Plane, Conjure Elemental, Creation, Destructive Wave, Flame Strike, Wall of Force
Lvl 6: Drawmij's Instant Summons, Guards and Wards, Sunbeam
Lvl 7: Delayed Blast Fireball, Divine Word, Fire Storm, Prismatic Spray
Lvl 8: Control Weather, Sunburst
Lvl 9: Meteor Swarm, Prismatic Wall

EADTHUUM (EARTH)

Cantrip: Blade Ward, Druidcraft, Mending, Prestidigitation (cannot create illusory object), Shillelagh, Thaumaturgy, Thorn Whip
Lvl 1: Armor of Agathys, Barkskin, Chromatic Orb, Ensnaring Strike, Entangle, Hail of Thorns, Identify, Mage Armor, Magic Missile, Purify Food and Drink, Unseen Servant
Lvl 2: Arcane Lock, Cloud of Daggers, Cordon of Arrows, Enlarge/Reduce, Knock, Magic Weapon, Pass Without Trace, Spider Climb, Spike Growth
Lvl 3: Conjure Barrage, Elemental Weapon, Glyph of Warding, Meld Into Stone, Plant Growth
Lvl 4: Conjure Minor Elementals, Fabricate, Grasping Vine, Stone Shape, Stoneskin
Lvl 5: Animate Objects, Contact Other Plane, Conjure Elemental, Conjure Volley, Creation, Passwall, Wall of Stone
Lvl 6: Blade Barrier, Disintegrate, Drawmij's Instant Summons, Flesh to Stone, Guards and Wards, Move Earth, Wall of Thorns
Lvl 7: Divine Word, Prismatic Spray
Lvl 8: Control Weather, Earthquake
Lvl 9: Imprisonment, Prismatic Wall

HALDORM (WATER)

Cantrip: Acid Splash, Poison Spray, Prestidigitation (cannot create illusory object), Ray of Frost, Thaumaturgy
Lvl 1: Chromatic Orb, Create or Destroy Water, Grease, Identify, Mage Armor, Magic Missile, Purify Food and Drink, Unseen Servant
Lvl 2: Arcane Lock, Magic Weapon, Melf's Acid Arrow, Misty Step
Lvl 3: Elemental Weapon, Glyph of Warding, Sleet Storm, Water Breathing, Water Walk
Lvl 4: Conjure Minor Elementals, Control Water, Fabricate, Ice Storm
Lvl 5: Contact Other Plane, Cone of Cold, Conjure Elemental, Creation
Lvl 6: Drawmij's Instant Summons, Guards and Wards, Otiluke's Freezing Sphere, Wall of Ice
Lvl 7: Divine Word, Prismatic Spray
Lvl 8: Control Weather, Tsunami
Lvl 9: Storm of Vengeance, Prismatic Wall

DAOVBEHNA (AIR)

Cantrip: Eldritch Blast, Message, Prestidigitation (cannot create illusory object), Shocking Grasp, Thaumaturgy, Witch Bolt
Lvl 1: Alarm, Chromatic Orb, Expeditious Retreat, Feather Fall, Fog, Identify, Mage Armor, Magic Missile, Thunderous Smite, Thunderwave, Unseen Servant
Lvl 2: Arcane Lock, Blindness/Deafness (only Deafness), Gust of Wind, Levitate, Magic Weapon, Shatter, Silence
Lvl 3: Blink, Call Lightning, Elemental Weapon, Fly, Gaseous Form, Glyph of Warding, Haste, Lightning Arrow, Lightning Bolt, Stinking Cloud, Wind Wall
Lvl 4: Conjure Minor Elementals, Dimension Door, Fabricate, Freedom of Movement
Lvl 5: Cloudkill, Contact Other Plane, Cone of Cold, Conjure Elemental, Creation, Destructive Wave, Telekinesis
Lvl 6: Arcane Gate, Chain Lightning, Drawmij's Instant Summons, Guards and Wards, Wind Walk
Lvl 7: Divine Word, Etherealness, Forcecage, Prismatic Spray, Reverse Gravity
Lvl 8: Control Weather, Incendiary Cloud
Lvl 9: Storm of Vengeance, Prismatic Wall

Nurhetic

The Nurhetic Tradition divides conceptually into Moon and Sun, representing Unconscious and Conscious aspects of the mind. Nurhetic mages used to divide themselves into strong philosophical camps on one or another side, but modern movements emphasize the harmony of these dimensions rather than disparity. Moon spells highlight Illusion and the imaginary, while Sun magic deals most of all with controlling thoughts and emotions.
Cantrip: Dancing Lights, Friends, Minor Illusion, Thaumaturgy
Lvl 1: Charm Person, Color Spray, Command, Compelled Duel, Detect Evil and Good, Detect Magic, Disguise Self, Dissonant Whispers, Heroism. Identify, Illusory Script, Silent Image, Sleep, Tasha's Hideous Laughter, Wrathful Smite
Lvl 2: Aid, Alter Self, Calm Emotions, Crown of Madness, Darkness, Enthrall, Invisibility, Mirror Image, Moonbeam, Phantasmal Force, See Invisibility, Suggestion
Lvl 3: Beacon of Hope, Clairvoyance, Fear, Hypnotic Pattern, Major Image, Modify Memory, Phantom Steed, Sending
Lvl 4: Arcane Eye, Compulsion, Greater Invisibility, Hallucinatory Terrain, Phantasmal Killer, Polymorph
Lvl 5: Awaken, Contact Other Plane, Dominate Person, Dream, Geas, Mislead, Rary's Telepathic Bond, Seeming
Lvl 6: Eyebite, Mass Suggestion, Otto's Irresistible Dance, Programmed Illusion
Lvl 7: Mirage Arcane, Project Image, Simulacrum
Lvl 8: Antipathy/Sympathy, Demiplane, Dominate Monster, Feeblemind, Mind Blank, Telepathy
Lvl 9: Shapechange, True Polymorph, Weird

Aurimbic

The Aurimbic Tradition is the least mappable to spells found in D&D. Roughly speaking, divination spells and those that deal with metamagic apply best, although the Tradition is more nuanced than this regarding world specifics. Because of this, Aurimbic mages figure more prominently as NPCs than PCs.
Cantrip: Guidance, Resistance, Thaumaturgy, True Strike, Vicious Mockery
Lvl 1: Bane, Bless, Detect Magic, Hunter's Mark, Identify, Mage Armor, Sanctuary, Shield, Shield of Faith
Lvl 2: Augury, Blur, Detect Thoughts, Find Traps, Locate Object, Magic Weapon, Nystul's Magic Aura, Zone of Truth
Lvl 3: Bestow Curse, Counterspell, Dispel Magic, Magic Circle, Nondetection, Protection From Energy, Remove Curse
Lvl 4: Confusion, Divination, Mordenkainen's Private Sanctum, Otiluke's Resilient Sphere, Staggering Smite
Lvl 5: Circle of Power, Contact Other Plane, Greater Restoration, Hallow, Legend Lore, Scrying
Lvl 6: Contingency, Find the Path, Forbiddance, Globe of Invulnerability, True Seeing
Lvl 7: Sequester, Symbol
Lvl 8: Antimagic Shell, Glibness, Maze
Lvl 9: Foresight, Wish

Exiled

The Exiled Tradition boasts spells that interweave Life, Death, and Time in a complex fashion. The majority of spells descend directly from Khajuro, whose magical workings have never been fully deciphered for the deep codes they contain. In brief, no spell of Khajuro's is fully what it seems to be, and most seem to secretly syphon magical energy "elsewhere" - another unknown.
Cantrip: Chill Touch, Spare the Dying, Thaumaturgy
Lvl 1: Cure Wounds, Detect Magic, Detect Poison and Disease, False Life, Healing Word, Hex, Identify, Inflict Wounds, Jump, Longstrider, Mage Armor, Ray of Sickness
Lvl 2: Blindness/Deafness, Enhance Ability, Gentle Repose, Hold Person, Lesser Restoration, Locate Animals or Plants, Prayer of Healing, Protection From Poison, Ray of Enfeeblement
Lvl 3: Animate Dead, Feign Death, Hunger of Hadar, Mass Healing Word, Revivify Slow, Speak With Dead, Spirit Guardians, Vampiric Touch
Lvl 4: Aura of Life, Aura of Purity, Aura of Vitality, Banishment, Blight, Death Ward, Evard's Black Tentacles, Guardian of Faith (spectral), Locate Creature
Lvl 5: Antilife Shell, Banishing Smite, Contact Other Plane, Contagion, Hold Monster, Mass Cure Wounds, Planar Binding, Raise Dead, Reincarnate
Lvl 6: Circle of Death, Create Undead, Harm, Heal, Magic Jar, Planar Ally (*special)
Lvl 7: Finger of Death, Plane Shift*, Regenerate, Resurrection
Lvl 8: Clone, Power Word Stun
Lvl 9: Astral Projection, Mass Heal, Power Word Heal, Power Word Kill, Time Stop, True Resurrection