Theory:

Animalia:
All the multicellular eukaryotic organisms which lack cell walls belong to the Kingdom Animalia.
These organisms are heterotrophic, and hence they rely on other organisms for their food. Most of the animals can move, unlike plants. They have a growth pattern by which the adult animals have a specific shape and size.
 
The majority of the animals have well-defined organ systems such as respiratory system, digestive system, excretory system etc., They also have a nervous system which is why they can respond to an external stimulus.
Classifications of Kingdom Animalia:
Classificationofanimals.svg
Classification of Kingdom Animalia
Coelom:
 
The fluid filled body cavity found between the alimentary canal and the body wall is known as coelom.
Based on the presence of a body cavity:
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Classification based on the coelom - The body cavity

Coelomates: The animals which have a true body cavity.

Pseudocoelomates: The animals which have a false body cavity.

Acoelomates: The animals which do not have a body cavity at all.
Based on the body symmetry:
The presence of body parts, in size, shape, and relative position, on opposite sides of a dividing line in the living organisms is known as body symmetry. Animals are classified  based on their body symmetry into three types. They are as follows:
 
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The plane of division in organisms
 
Radial symmetry: A symmetry in which the sides exhibit regularity of parts around a central axis is known as radial symmetry.
  
Bilateral symmetry: The form of symmetry in which the opposite sides are similar.
  
Asymmetry: The lack or absence of symmetry.
Based on the presence and absence of the vertebral column:
The organisms of Kingdom Animalia are classified into two categories such as invertebrates and vertebrates on the presence and absence of a vertebral column.
 
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Vertebrates and invertebrates
 
Invertebrates:
  
Sponges, hydra, flatworms round worms, insects, snails, starfishes are some of the invertebrates due to the absence of a vertebral column.
 
Vertebrates:
  
Fish, amphibians, reptiles, birds, and mammals including human beings are some of the vertebrates due to the presence of a vertebral column.
Reference:
https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Figure_27_02_05.jpg/512px-Figure_27_02_05.jpg
https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Figure_33_01_01.jpg/1024px-Figure_33_01_01.jpg
https://www.flickr.com/photos/121935927@N06/13578745783