Hypabyssal igneous rocks are formed at a depth in between the plutonic and volcanic rocks. These are formed due to cooling and resultant solidification of rising magma just beneath the earth surface. Hypabyssal rocks are less common than plutonic or volcanic rocks and often form dikes, sills, laccoliths, lopoliths, or phacoliths.
Igneous rocks are classified according to mode of occurrence, texture, mineralogy, chemical composition, and the geometry of the igneous body.
The classification of the many types of different igneous rocks can provide us with important information about the conditions under which they formed. Two important variables used for the classification of igneous rocks are particle size, which largely depends upon the cooling history, and the mineral composition of the rock. Feldspars, quartz or feldspathoids, olivines, pyroxenes, amphiboles, and micas are all important minerals in the formation of almost all igneous rocks, and they are basic to the classification of these rocks. All other minerals present are regarded as nonessential in almost all igneous rocks and are called accessory minerals. Types of igneous rocks with other essential minerals are very rare, and these rare rocks include those with essential carbonates.
In a simplified classification, igneous rock types are separated on the basis of the type of feldspar present, the presence or absence of quartz, and in rocks with no feldspar or quartz, the type of iron or magnesium minerals present. Rocks containing quartz (silica in composition) are silica-oversaturated. Rocks with feldspathoids are silica-undersaturated, because feldspathoids cannot coexist in a stable association with quartz.
Igneous rocks which have crystals large enough to be seen by the naked eye are called phaneritic; those with crystals too small to be seen are called aphanitic. Generally speaking, phaneritic implies an intrusive origin; aphanitic an extrusive one.
An igneous rock with larger, clearly discernible crystals embedded in a finer-grained matrix is termed porphyry. Porphyritic texture develops when some of the crystals grow to considerable size before the main mass of the magma crystallizes as finer-grained, uniform material.
We will classify igneous rocks on the basis of texture and composition. Texture refers to the size, shape and arrangement of the mineral grains or crystals of which the rock is composed.
Texture is an important criterion for the naming of volcanic rocks. The texture of volcanic rocks, including the size, shape, orientation, and distribution of mineral grains and the intergrain relationships, will determine whether the rock is termed a tuff, a pyroclastic lava or a simple lava.
However, the texture is only a subordinate part of classifying volcanic rocks, as most often there needs to be chemical information gleaned from rocks with extremely fine-grained groundmass or from airfall tuffs, which may be formed from volcanic ash.
Textural criteria are less critical in classifying intrusive rocks where the majority of minerals will be visible to the naked eye or at least using a hand lens, magnifying glass or microscope. Plutonic rocks tend also to be less texturally varied and less prone to gaining structural fabrics. Textural terms can be used to differentiate different intrusive phases of large plutons, for instance porphyritic margins to large intrusive bodies, porphyry stocks and subvolcanic dikes (apophyses). Mineralogical classification is used most often to classify plutonic rocks. Chemical classifications are preferred to classify volcanic rocks, with phenocryst species used as a prefix, e.g. "olivine-bearing picrite" or "orthoclase-phyric rhyolite".
Chemical classification
Igneous rocks can be classified according to chemical or mineralogical parameters:
Chemical: total alkali-silica content (TAS diagram) for volcanic rock classification used when modal or mineralogic data is unavailable:
    felsic igneous rocks containing a high silica content, greater than 63% SiO2 (examples granite and rhyolite)
    intermediate igneous rocks containing between 52 – 63% SiO2 (example andesite and dacite)
    mafic igneous rocks have low silica 45 – 52% and typically high iron – magnesium content (example gabbro 
    and basalt)
    ultramafic rock igneous rocks with less than 45% silica. (examples picrite, komatiite and peridotite)
    alkalic igneous rocks with 5 – 15% alkali (K2O + Na2O) content or with a molar ratio of alkali to silica    
    greater than 1:6. (examples phonolite and trachyte)
Chemical classification also extends to differentiating rocks which are chemically similar according to the TAS diagram, for instance;
    Ultrapotassic; rocks containing molar K2O/Na2O >3
    Peralkaline; rocks containing molar (K2O + Na2O)/ Al2O3 >1
    Peraluminous; rocks containing molar (K2O + Na2O)/ Al2O3 <1
An idealized mineralogy (the normative mineralogy) can be calculated from the chemical composition, and the calculation is useful for rocks too fine-grained or too altered for identification of minerals that crystallized from the melt. For instance, normative quartz classifies a rock as silica-oversaturated; an example is rhyolite. In an older terminology silica oversaturated rocks were called silicic or acidic where the SiO2 was greater than 66% and the family term quartzolite was applied to the most silicic. A normative feldspathoid classifies a rock as silica-undersaturated; an example is nephelinite.
Mineralogical classification
For volcanic rocks, mineralogy is important in classifying and naming lavas. The most important criterion is the phenocryst species, followed by the groundmass mineralogy. Often, where the groundmass is aphanitic, chemical classification must be used to properly identify a volcanic rock.
felsic rock, highest content of silicon, with predominance of quartz, alkali feldspar and/or feldspathoids: the felsic minerals; these rocks (e.g., granite, rhyolite) are usually light coloured, and have low density.    mafic rock, lesser content of silicon relative to felsic rocks, with predominance of mafic minerals pyroxenes, olivines and calcic plagioclase; these rocks (example, basalt, gabbro) are usually dark coloured, and have a higher density than felsic rocks.
    ultramafic rock, lowest content of silicon, with more than 90% of mafic minerals (e.g., dunite).
For intrusive, plutonic and usually phaneritic igneous rocks where all minerals are visible at least via microscope, the mineralogy is used to classify the rock. This usually occurs on ternary diagrams, where the relative proportions of three minerals are used to classify the rock.
Magma evolution
Most magmas only entirely melt for small parts of their histories. More typically, they are mixes of melt and crystals, and sometimes also of gas bubbles. Melt, crystals, and bubbles usually have different densities, and so they can separate as magmas evolve.
As magma cools, minerals typically crystallize from the melt at different temperatures (fractional crystallization). As minerals crystallize, the composition of the residual melt typically changes. If crystals separate from melt, then the residual melt will differ in composition from the parent magma. For instance, a magma of gabbroic composition can produce a residual melt of granitic composition if early formed crystals are separated from the magma. Gabbro may have a liquidus temperature near 1200 °C, and derivative granite-composition melt may have a liquidus temperature as low as about 700 °C. Incompatible elements are concentrated in the last residues of magma during fractional crystallization and in the first melts produced during partial melting: either process can form the magma that crystallizes to pegmatite, a rock type commonly enriched in incompatible elements. Bowen's reaction series is important for understanding the idealised sequence of fractional crystallisation of a magma.
Magma composition can be determined by processes other than partial melting and fractional crystallization. For instance, magmas commonly interact with rocks they intrude, both by melting those rocks and by reacting with them. Magmas of different compositions can mix with one another. In rare cases, melts can separate into two immiscible melts of contrasting compositions.
There are relatively few minerals that are important in the formation of common igneous rocks, because the magma from which the minerals crystallize is rich in only certain elements: silicon, oxygen, aluminium, sodium, potassium, calcium, iron, and magnesium. These are the elements which combine to form the silicate minerals, which account for over ninety percent of all igneous rocks. The chemistry of igneous rocks is expressed differently for major and minor elements and for trace elements. Contents of major and minor elements are conventionally expressed as weight percent oxides (e.g., 51% SiO2, and 1.50% TiO2). Abundances of trace elements are conventionally expressed as parts per million by weight (e.g., 420 ppm Ni, and 5.1 ppm Sm). The term "trace element" typically is used for elements present in most rocks at abundances less than 100 ppm or so, but some trace elements may be present in some rocks at abundances exceeding 1000 ppm. The diversity of rock compositions has been defined by a huge mass of analytical data—over 230,000 rock analyses can be accessed on the web through a site sponsored by the U. S. National Science Foundation (see the External Link to EarthChem).
The word "igneous" is derived from the Latin ignis, meaning "of fire". Volcanic rocks are named after Vulcan, the Roman name for the god of fire. Intrusive rocks are also called "plutonic" rocks, named after Pluto, the Roman god of the underworld.

Source: wikipedia.org