The Multiverse is a local set of many unique Universes under a given continuous series of laws and is also the second in a series of Archverses. Uniqueness isn't mandatory but is guaranteed due to the sensitivity of conditions during Universe formation. The biggest multiverse is registered as MLTI-577, and the smallest one is knowm as MLTI-183. Most of them are contained by Megaverses.
Each Universe in a Multiverse, as stated above, shares in common laws of physics, systems of nature, sets of elementary particles and all other laws of the parent Multiverse. However, since each Universe varies in initial conditions, the entire timeline is affected and entire cosmological structures are "reshuffled", so to speak.
We can use our own Universe as an example of ways other Universes vary in more than just timelines. For example, if the initial conditions are different enough, the ratio of matter to dark matter can be affected, the ratio between matter and anti-matter can change, and sometimes, it is possible that even constants can change by very tiny amounts, like the fine structure constant being very slightly different.
Finite multiverses average in size around 8 quadrillion light-years, making our Multiverse slightly above average in diameter. Multiverses are also 4 dimensional, meaning that even though Universes are quite far away from each other, despite not moving much, and there being copious amounts in each Multiverse, they still very rarely collide with one another and have a lot of space, whilst moving through 4 axis.
Similar to Universes, Multiverses have their own entire natural systems and structures, just like Universes. They are a byproduct of their Universes, so if a particularly strange and "mutated" Universe forms naturally within its Multiverse, it will have a strong impact on its surrounding ecosystem. However, most Multiverses have similar Universes, therefore they also appear to be homogeneous.
The size of Multiverses varies and the contents are loads and loads of different Universe with different laws of nature. The multiverse can contain parallel Universes. For example, maybe there is a Universe parallel to ours where Hitler won the War, or where dinosaurs didn't go extinct, or where humans aren't an intelligent species at all. There may also be tons of Universes that are parallel to being parallel to others, meaning that two different changes occur compared to each other. Perhaps this chain goes on forever.
Multiverses do not only contain Universe, but they can also contain their own space and time outside a Universe and maybe their own material. They may also have laws of nature, space, time, events, etc. completely inside themselves, unaffected and not limited to the universes within them.
Upon the conception of the Proto-Xenoverse, instead of it being a perfect sphere, it becomes a tangled and disordered 6-dimensional object. When mapped onto the 3rd dimension, the 3D surface crosses itself upon random points. In reality, these points are 4D Multiverses of deformed shape.
As the Proto-Xenoverse expands and pulls these folds back, eventually becoming an actual Xenoverse, they snap and decay, turning into Metaverses, as they degenerate into the lower 5th dimension, and their crossings become the 4th-dimensional Multiverses. Every fold captures the crossings that it went through, which gives the Metaverses their own Multiverses right upon birth.
The chaotic nature of the Xenoverse generates sets of laws, like encrypted random quantum fluctuations, when processed properly, which is exactly what the folds and crossings do. However, there are many other ways to do it, other than the natural everyday process, which is how most artificial Metaverses and Multiverses used to be made (new technological advancements have made this process more and more antiquated).
Max Tegmark, a proponent of Hugh Everett's many-worlds interpretation, expanded upon his ideas from Everett's original quantum mechanics, which removes wave function collapse and asserts a Multiverse filled with Universes, where each possible observable outcome correlates to a Universe. In essence, all random quantum-state outcomes already exist, in a sort of library of Babel type way.
A level 1 Multiverse contains an infinite number of Universes of this above-mentioned property.
A level 2 Multiverse is a sort of Metaverse equivalent, which contains bubbles, those being level 1 Multiverses. Level 2 Multiverses may experience spontaneous symmetry breaking, which can change physical constants.
A level 3 Multiverse is simply another break in symmetry from the lower level Multiverses.
The level 4 Multiverse is the final in the series, containing everything describable by mathematical structures, as Tegmark believes reality is purely mathematical.
Levels 1, 2, and 3 are conceptually all equivalent.
Lee Smolin's fecund Universes
Lee Smolin, in his 1992 book The Life of the Cosmos, proposed a theory, that a black hole's collapse creates a new universe on the "other side" of the black hole (possibly a white hole's reality/exit), with slightly changed parameters of physical constants.
In this way, Universes give metaphorical birth to other Universes, passing down their "genes", with failing Universes simply relapsing, whilst stable ones live further. This theory is also called Cosmological natural selection.
Brian Greene's 9 types
Quilted: infinite in size, every single event happens, however, the speed of light limits us from seeing any others beyond our Universe
Inflationary: an eternally inflating Multiverse is comprised of bubble-like pockets, which collapse to form Universes
Brane: each Universe is constricted to a brane within a higher dimensional Multiverse, in which said Universes freely flow around, colliding on rare occasions and producing new big bangs. This is the type primarily described within this article.
Cyclic: an extension to the brane Multiverse, where "the universes bounce back and pass through time until they are pulled back together and again collide, destroying the old contents and creating them anew." 1
Landscape: a Multiverse comprised of a false vacuum landscape creates Universes from quantum fluctuations.
Quantum: a many-world interpretation, but the Universes are created each time a wave collapse happens.
Holographic: the Multiverse is based on the holographic principle (aka: the surface encodes the volume).
Simulated: a Multiverse simulated on a complex computer system.
Ultimate: the ultimate Multiverse contains every mathematically possible Universe, equivalent to Max Tegmark's level 4 Multiverse.
Black hole cosmology
Black hole cosmology, similarly to Lee Smolin's fecund Universes, states that Universes exist within black holes. However, fecund Universes are created upon the collapse of a black hole, effectively creating Archverses, whilst black hole cosmology brings the Universe inside the black hole upon the black hole's conception. Under this theory, a black hole can have many Universes, not just one, basically becoming a Universe cluster.