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As I intended, I maxed out all the skills of one character to 100. I didn't rush, so it took about 130 hours. Now I want to describe my observations; I hope they will be useful to someone.
Combat Skills
Skills like One-Handed, Two-Handed, Archery, and Destruction are leveled only by dealing damage; I didn't find any tricks. Leveling these skills seemed to take the longest, so I recommend using trainers. Also, it might be worth increasing the difficulty level if your equipment allows it: enemies will become tougher, requiring more hits, so the skill will increase faster than if you visit different dungeons to find more enemies.
Defensive Skills
Skills like Light Armor, Heavy Armor, and Block are leveled only by taking damage, and Block is leveled by taking damage with a raised shield or a two-handed weapon in a defensive stance (right-click). There is a way to force the skill to level up: go to the giant's camp, leave one alive, and stand under its attacks, replenishing your health with potions or magic (this is an obvious but not the most effective way to level Restoration). Instead of a giant, you can use any strong enemy, such as a Falmer mercenary or a bandit leader. Defensive skills will also level up much faster if you increase the game's difficulty.
Sneak
Again, a very straightforward skill. Fortunately, it is unique and levels up much faster than combat skills. To level it, I recommend spending 90% of the time in stealth, both in dungeons and in cities.
Crafting Skills
Enchanting is leveled based on the number of items created, so it is optimal to collect light items like rings and leather bracers and enchant them with small soul gems purchased from mages. If you enchant and sell jewelry, you can even make a profit.
When leveling Smithing and Alchemy, the value of the created item is taken into account, so it is advisable to choose more expensive recipes. At levels 15-80, the fastest way to level Smithing is by crafting jewelry. To get a large number of silver and gold ingots, it is worth learning the "Transmute" spell. Iron ore can be bought from any blacksmith in the cities. Starting from skill level 80, the most optimal will be to double-improve first Ebony, and then Daedric items. Double-improvement can be done as follows: craft or find an item, improve it by taking the corresponding perk in the skill tree, then drink a potion to increase the Smithing skill (sold in alchemy shops), and improve the item again. We improve twice, not at once, because for each time, experience is awarded, as for creating a new item.
For leveling Alchemy, I highly recommend investing skill points in the first perk in the tree, which increases the effect of all potions, and with it, their value. We pick up all the reagents scattered around the world, buy the entire assortment in alchemy shops, craft potions, and sell them. If you invest 5 skills in the tree, the income will be extremely high.
Magic
To level Restoration, Illusion, Alteration, and Conjuration, I recommend first making the corresponding schools of magic free. To do this, you need to invest 6 skill points in Enchanting and enchant four items (armor, helmet, ring, and necklace) to reduce the cost of spells of the corresponding school. Then, constantly use the spell: Restoration - Ward, Illusion - Muffle, Alteration - Transmute and Detect Life (it is better to stand somewhere in the center of the city), Conjuration - summon and dismiss a weapon while in combat. If you don't want to engage in a real fight to level Conjuration, you can summon any creature and start hitting it: then it will become hostile.
Utility Skills
Pickpocket - we steal things from everyone, preferably more expensive ones. You can combine leveling Pickpocket with leveling any other skill: find a trainer, save, learn one level, and steal the money for the training. Repeat until skill 51: the cost of increasing the skill level after 51 exceeds 1500, and this amount cannot be stolen without investing skill points in Pickpocket.
Lockpicking - we open everything we see, without taking keys with us so as not to skip locks. You can visit the Jarl's chambers in Dragonreach and Jorvaskr once a month: there are many locks of "Expert" and "Master" level. Once a month - because all locations are updated with this period.
To level Speech, you need to sell a lot of valuable items. In my opinion, a very effective method is to craft and improve a dragonbone warhammer and sell it to a trainer to whom you have given more than 20,000 septims for lessons. To do this, it is highly desirable to take a perk in the tree that allows you to sell any items to any merchants. It greatly simplifies life when you need to get rid of unnecessary items made yourself or found in dungeons. Also, for leveling Speech, in dialogues, first use the replics marked "Persuasion" or "Intimidation", and then other options.
Class Change
For owners of the Legendary Edition and/or the Dragonborn DLC, the developers have provided a legal way to change classes. If you have the Legendary Edition, you can reset a skill leveled to 100 to 15 and get back all the skill points invested in the tree of that skill. The skill can be leveled up to 100 again and made legendary again (that is, the level is reset, and the points are returned). Thus, in the Legendary Edition, the level limit of 81 is removed. To get all the perks in all 18 trees, you need to make 147 legendary skills.
In Dragonborn, after completing the Mirrak storyline, you can reset skill points for 1 dragon soul. The skill level remains the same.
Changing classes can be useful if you get tired of using the same type of weapon, but you don't want to start a new game. This can happen, as even on "Novice", to level up one combat skill to 100, you need to clear less than a third of the dungeons of the original game (Dragonborn adds more than 30 new dungeons).
Over-Enchanting
Caution: the information below may spoil the enjoyment of the game.
By combining the effects of enchantments, potions, and item improvements, you can achieve truly amazing results in improving the character's combat abilities. First of all, you need to level up Alchemy, Enchanting, and Smithing to 100, invest 6 skill points in Enchanting (Enchanter 1-5, Skill Charms), 5 - in Alchemy (Alchemist 1-5), 5 - in Smithing (learn Dragon Armor). Then, you need to create a potion that increases the enchanting skill, then enchant four items to increase alchemy, then brew a potion again, and so on. When you think the improvement is sufficient, instead of enchanting to increase alchemy, make an enchantment to increase smithing, and also brew a potion with a similar effect. Forge a set of your favorite dragon armor, your favorite type of weapon, improve it, and then enchant it to increase damage or reduce spell cost. If you take the "Extra Effect" perk in the Enchanting tree, one set of armor can make three schools of magic free or increase damage from two types of weapons.