Level 1
ST 6 PE 5 EN 5 CH 1 IN 10 AG 7 LK 6
Medicine, Science, and Lockpick
Grognak the Barbarian => Melee Weapons +1 (18)
Level 2
Sneak +5 (24), Lockpick +5 (35), Melee Weapons +10 (28)
Daddy's Boy/Girl
Level 3
Sneak +5 (29), Lockpick +5 (40), Explosives +5 (20), Melee Weapons +5 (33)
Daddy's Boy/Girl
Level 4
Sneak +5 (34), Lockpick +5 (45), Explosives +5 (25), Melee Weapons +5 (38)
Educated
Level 5
Sneak +6 (40), Lockpick +5 (50), Repair +5 (30), Melee Weapons +7 (45)
Daddy's Boy/Girl
Level 6
Sneak +5 (45), Lockpick +5 (55), Speech +3 (10), Melee Weapons +10 (60)
Little Leaguer
Level 7
Sneak +5 (50), Lockpick +5 (60), Barter +3 (10), Science +5 (60), Melee Weapons +5 (70)
Little Leaguer
Level 8
Small Guns +1 (20), Lockpick +5 (65), Speech +2 (12), Repair +5 (35), Science +5 (65), Melee Weapons +5 (80)
Little Leaguer
Level 9
Lockpick +5 (75), Speech +3 (15), Repair +5 (40), Science +5 (70), Melee Weapons +5 (85)
Thief
Level 10
Sneak +5 (65), Barter +3 (13), Science +5 (75), Melee Weapons +5 (90), Medicine +5 (60)
Thief
Level 11
Small Guns +5 (25), Repair +3 (43), Explosives +5 (45), Science +5 (80), Medicine +5 (65)
Thief
Level 12
Small Guns +5 (35), Repair +7 (55), Explosives +5 (50), Barter +1 (14), Science +5 (85)
Gun Nut
Level 13
Lockpick +5 (90), Speech +6 (21), Barter +7 (21), Science +5 (90)
Gun Nut
Level 14
Sneak +5 (75), Small Guns +5 (50), Speech +3 (24), Explosives +5 (55), Medicine +5 (70)
Gun Nut
Level 15
Speech +1 (25), Repair +10 (75), Explosives +5 (60), Barter +2 (23), Big Guns +5 (20)
Silent Running
Level 16
Sneak +5 (90), Small Guns +5 (55), Explosives +5 (65), Barter +3 (26), Big Guns +5 (25)
Tag! (Unarmed)
Level 17
Small Guns +10 (65), Explosives +5 (70), Barter +3 (29), Medicine +5 (75)
Iron Fist
Level 18
Small Guns +5 (70), Energy Weapons +5 (20), Barter +3 (32), Medicine +5 (80), Big Guns +5 (30)
Iron Fist
Level 19
Small Guns +5 (75), Energy Weapons +5 (25), Repair +5 (80), Barter +8 (40)
Iron Fist
Level 20
Small Guns +5 (80), Energy Weapons +3 (28), Unarmed +5 (35), Explosives +5 (75), Big Guns +5 (35)
Bloody Mess
Level 21
Energy Weapons +7 (35), Explosives +5 (80), Barter +1 (41), Big Guns +10 (60)
Size Matters
Level 22
Energy Weapons +15 (50), Barter +3 (44), Medicine +5 (85)
Size Matters
Level 23
Energy Weapons +10 (60), Unarmed +7 (42), Barter +6 (50)
Size Matters
Level 24
Energy Weapons +15 (85), Unarmed +3 (45), Barter +5 (55)
Cyborg
Level 25
Unarmed +3 (48), Speech +20 (45)
Pyromaniac
Level 26
Unarmed +8 (56), Speech +10 (55), Barter +5 (60)
Finesse
Level 27
Unarmed +8 (64), Speech +5 (60), Barter +10 (70)
Ninja
Ant Sight
Level 28
Unarmed +7 (71), Speech +11 (71), Barter +5 (75)
Sniper
Level 29
Unarmed +9 (80), Speech +9 (80), Barter +5 (80)
Contract Killer
Level 30
Small Guns +5 (91), Unarmed +2 (92), Speech +3 (100), Repair +5 (87), Explosives +3 (93), Barter +5 (100)
Almost Perfect
Bobblehead (Strength)
Bobblehead (Perception)
Bobblehead (Endurance)
Bobblehead (Charisma)
Bobblehead (Intelligence)
Bobblehead (Agility)
Bobblehead (Luck)
Bobblehead (Repair)
Bobblehead (Science)
Bobblehead (Medicine)
Bobblehead (Barter)
Bobblehead (Big Guns)
Bobblehead (Energy Weapons)
Bobblehead (Explosives)
Bobblehead (Lockpick)
Bobblehead (Melee Weapons)
Bobblehead (Small Guns)
Bobblehead (Sneak)
Bobblehead (Speech)
Bobblehead (Unarmed)
D.C Journal of Internal Medicine
Dean's Electronics
Which can be done for all skills which have up to 25 books possible, which the exception of Barter which has 23. For locations check the Fallout wiki page.