MORPHOLOGY

A. The Different Between Morpheme and Allomorphs 
Morpheme is the smallest linguistic unit that has semantic meaning. E.g. The word "unbreakable" has three morphemes: "un-" (meaning not x), a bound morpheme; "-break-", a free morpheme; and "-able", a free morpheme. "un-" is also a prefix, "-able" is a suffix. Both are affixes.
Allomorphs are the different representation (VARIANT) of morpheme with the same meaning. E.g the morpheme plural-s has the morph "-s", IPA: [s], in cats ([kæts]), but "-es", [ɪz], in dishes ([dɪʃɪz]), and even the voiced "-s", [z], in dogs ([dɒgz]). These are the allomorphs of "-s"
B. The Types of Morpheme 
Free morphemes are the morphemes which can stand alone as single words. E.g. “free” and “close”. These morphemes are divided into two kinds of morphemes. The first is the set of ordinary nouns, adjectives and verb that is called lexical morpheme. The examples are: man, beautiful, sing, and funny. The other one is called functional morphemes that consist of functional words such as conjunctions, pronouns, articles and prepositions and the examples are because, at, on, near, the, a, this. Bound morphemes are the morphemes which normally can’t stand alone but typically attached to another form. E.g re-, -ist, un-, -ed, -s. Bound morphemes are also divided into two types. 1. Derivational morphemes are used to make a new word in language. 2. Inflectional morphemes are not used to make new words of English language.
C. The Difference Between Stem and Root
Stem, being also called inflectional root, is the part of a word that is common to all its inflected variants. The example, the root of the English adjective form unbreakable is break and the stem is un-break-able, which include derivational affixes un- and –able. Root is the primary lexical unit of a word, that cannot be reduced into smaller constituents. It carries the most significant aspects of semantic content. The example, the root of the English verb form sleeping is sleep.

D. The Affixation and Its Types
Affixation is the result of the process of words forming by the combination of bound affixes and free morpheme. The types of affixations are:
Compounding, that is a process of words forming from two or more independent words. The example, notebook, boyfriend. Reduplication is a process that forms new words either by doubling an entire free morpheme (total reduplication) or part of it (partial reduplication). The example is willy-nilly. Morpheme-internal changes is a process of forming new words by morpheme-internal modification. The example are; mice-mouse, thief-thieves, go-went-gone. Suppletion is the process of forming new words irregularly. Those processes are exceptions. The example; run [rΛn]- ran [ræn].
E. Inflectional and Derivational Affixes
Inflectional affixes are affixes that are not used to make new words of English language and they can’t change in meaning. They can be suffixes (-s, -ing, -ed, -er, -est etc). Derivational affixes are affixes that are used to make new words and they can change in meaning. they can suffixes (-en, -able, -ful, -ment, -ion, -ize etc) or prefixes (en-, mis-, de-, un-, dis- etc).
F. Word Formation
Word formation is the ways of new words forming from bound and free morpheme. The combinations of bound and free morpheme are systematic. The example; the suffix –able, meaning “can” attaches only to adjectives, the prefix -nees attaches only to nouns, the suffix mis- attaches only to nouns etc.

Bibliography
Nasr, Raja T, The Essential of Linguistic Science, Longman House, Harlow, London, England, 1984.
Lyons, John, Language a Linguistic and Introduction, Cambridge University, New York, 1984.
Yule, George, The Study of Language an Introduction, Britanian: Cambridge University Press, 1985.
Jannedy, Stefanie cs, Language Files, Columbus: Ohio State University, 1994. 
http://en.wikipedia.org/wiki/Morphology_(linguistics)