Basically mfossils are classified as mineral (silicious, phosphatic, carbonate etc) and organic walled based on their exoskeleton composition.
Shell such as that of molluscs or echinoderms, is composed of calcium carbonate
(CaCO3). Most calcium carbonate shell tissue is the mineral calcite, the same mineral
that composes the sedimentary rock limestone. Calcite is a relatively stable mineral.
Some invertebrates secrete a shell made of aragonite, which is a high pressure
polymorph of calcium carbonate. Mother-of-pearl, true pearls, and many mollusc shells
are composed of this relatively unstable mineral, which tends to recrystallize to its more
stable cousin calcite, or simply dissolve.

Opaline Silica, a cryptocrystalline or amorphous form of hydrated silicon dioxide
(SiO2•nH2O; similar to the mineral quartz), composes the hard tests or shells of
microorganisms such as diatoms and radiolarians as well as the spicules of some
sponges. Many bedded cherts originate as accumulations of the tests or spicules of
many millions of these organisms.

Bone in vertebrate animals is composed of about 85% calcium phosphate, called by the
mineral name hydroxyapatite (Ca5(PO4)3•nH2O). The remaining 15% is organic
material. Hydroxyapatite is very stable in most near-surface geological environments,
and, once buried, is easily preserved.
Chitin is a complex carbohydrate that makes up the shells or exoskeletons of many
arthropods, the phylum of organisms that includes insects and crustaceans. It is also
common in many inarticulated brachiopods and fungi. Chitin is normally not preserved
except in organisms where it is strengthened with calcium carbonate or calcium
phosphate.

Cellulose and lignin are carbohydrates that compose the hard tissues and wood of
plants. Some herbaceous plants strengthen their tissues with opaline silica, which favors
their preservation in the fossil record. Woody plants are strengthened with the
carbohydrate lignin, which sometimes retains its structure long enough to allow
permineralization of surrounding pores.
Application can be various from palaeoclimate analysis to Ocean water composition and many more.
Mode of formation includes the way the hard parts get preserved in time. there are various ways

1. Preservation without alteration
2. Pecrystallization
3. Permineralization
4. Replacement
5. Carbonization
6. Molds and cast,

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