While the term phonetics relates to 'detailed analysis of the sounds and sound production of the human race', phonology focuses on 'speech sounds which belong to a particular language system'; hence the phrases "English phonology" and "French phonology". You may come across books on "The Phonetics of French". Such a title implies "a detailed study in acoustic terms from the point of view of substance rather than meaning." However, it is more than likely that the focus will be on French phonology i.e. in the context of meaning.
Phonemes belong to given language systems, so while phonetic script can be used to transcribe the sounds of all known languages, the British English phonemic alphabet just contains the 44 symbols needed to transcribe British English. It would therefore be inefficient to teach a learner of English the vast number of symbols in the phonetic alphabet since is unlikely that they would want to transcribe all the known languages in the world.
Some linguists define a phoneme as 'the smallest meaningful unit of sound'; hence the phonemes /θ/ and / s / are the initial English consonant sounds which differentiate meaning in the words "think" and "sink" respectively. A native French speaker may find it difficult at first to differentiate between the English phonemes /θ/ and / t / when attempting to pronounce the initial consonant sound in the word "theatre", since there is no phoneme sufficiently similar to the English phoneme /θ/ in French phonology.
When comparing language systems, L1 relates your native language, and L2 to a second language (e.g. English if you are learning it and it isn't your mother tongue)
"Unless the teacher understands how the student is using his speech organs in producing a native language sound and what he should be doing to reproduce the foreign language sound acceptably, he cannot help the student beyond a certain stage of earnest but inaccurate imitation." [Wilga Rivers - Teaching Foreign Language Skills]
Can your teacher tell you how many phonemes there are in the English language and how to use your organs of articulation to produce these sounds?
Teachers who have studied the sound system of your L1 will also be in a better position to help you with common mistakes in L2 (e.g. English).
I have added pages on the 12 English Monophthongs and the 8 English Diphthongs. The page on monophthongs shows the fixed tongue positions (the height of the front or the back of the tongue and the degree of retraction) for producing these sounds in Received Pronunciation. The tongue travels between some of these fixed positions to produce the diphthongs. Learners often find the 5 long English vowel sounds and the diphthongs difficult to produce, since learners' native languages more commonly feature most of the short English vowel sounds.
Word lists to practise Consonant Clusters
When there are three or more consonants together, native speakers do not always produce as many consonant sounds. For example, the final consonant cluster in the word "fifths" is usually reduced to the last two consonant phonemes. Good pronunciation materials need to include practice of elision (missing phonemes out) and assimilation (a change in the quality of the phoneme - perhaps to a different phoneme altogether!).
Some English consonant sounds, including many alveolar ones, change into (or towards) different phonemes when followed by certain other sounds. Speakers assimilate to avoid awkward sound combinations which would lead to loss of oral fluency with utterances sounding broken up and clumsy. Some native English speakers, including those who have been to top schools, are ignorant of the differences between written and spoken English and attempt to speak as they write. The remedy is Assimilation Practice. The links below provide learners with short phrases where assimilation occurs: