Mods/Thaumcraft/Aspects

Aspects are the "flavors" of magic, affecting all its forms. Most importantly, ../vis/, ../essentia/, and ../Research Points come in all the various aspects, with only limited conversion among types. There are 6 Primal aspects (Aer (air), Terra (earth), Ignis (fire), Aqua (water), Ordo (order), and Perditio (entropy)), which combine in various ways to produce 44 Compound Aspects, for a total of 50.

Some aspect combinations have changed between versions 4.10 and 4.11 of Thaumcraft (some aspects were removed), and again for 4.2.2. [This "research helper"] lists the compositions of all aspects for versions 4.10g, 4.11.9, and 4.11.14, which are the versions when they changed.

Uses

 * Vis, the "gaseous" form of magic, can be drawn into wands and stored. Once in the wand, these can be used in various magical craftings.   Normally vis is drawn from nodes, but small amounts are also scattered every time a mob is killed -- if a nearby player has a wand in their hotbar, the wand will try to absorb these, subject to its capacity.  Vis comes in all aspects, but only primal aspects can be stored in a wand.  With proper equipment, a compound node can be tapped by a wand, but the wand will get primal vis based on the compound aspect's components.
 * Essentia, the "liquid" form of magic, is produced by breaking down material objects, stored in phials and warded jars, and used for crafting, enchanting, and powering various devices.  Essentia cannot be combined aspect-wise (for example, you cannot combine Terra and Aqua vis to make Victus), but with appropriate devices (../centrifuge/ or even a ../crucible/), essentia of a compound aspect can be broken up into its components.  Note that for each point of a compound aspect, you will get only one point of one of the components. With further research it can be stored in a crystalline form.
 * Research points are gained in particular aspects (mostly from the ../Thaumometer/), and used to research things relevant to their nature. In contrast to the magical uses, research points for compound aspects cannot be separated, but points can be combined aspect-wise.  (You only get one point of the compound, for a point apiece of each component.)

Aspects and Items
Each item (also mobs, blocks, and entities) also has one or more aspects. These can be revealed (and earned as research points) by scanning them, For items, their aspects can be extracted to essentia by a ../Cauldron/ or ../Alchemical Furnace/, then used for other processes. Mobs can be subjected to something similar, by the advanced item Liquid Death, which drops their aspects as essentia crystals.

Below is a list of the best items to get aspects wholesale. Some entries also mention a type of essentia they can be centrifuged from, which is itself easy to get. Two items are particularly important for advanced players, as between them, they renewably provide essentia aspects that are most needed in large quantities: Early on, Charcoal provides Ignis for the Infernal Furnace, and Potentia for the Thaumostatic Harness. Later, netherwart provides Praecantio for making thaumium and many other enchantments, and Herba for the Lamp of Growth. (This leaves the Arcane Bore, whose thirst for Perditio can be met with cobblestone stairs or cactus.)

A tip for tools, boats and other things that don't stack: The arcane workbench holds items in place even when the GUI is not open. Arrange enough source materials for the desired quantity, take as many as your inventory will hold, load them into a hopper connected to the arcane furnace, and keep collecting from the workbench as you free up inventory space.

All types of essentia can also be obtained from mana beans and, to a lesser extent, ethereal essence.

Cheat Sheets

 * This page at FTB lists the combinations for all the aspects, including those from common addons (sub-mods for Thaumcraft). It also gives sources for many of them.