Though both StoneyB's answer and FumbleFinger's comment have already discussed the four "the"s in your question, I would like to provide additional information about articles, in hope that it'd be useful.
Using articles properly is difficult for learners, especially the learners who speak languages that do not have articles. Thus, it's very useful for these learners (myself included) to know the "two basic rules" listed in Practical English Usage by Michael Swan, under entry 62.1:
- To say 'You know which I mean', we put the before a noun.
I've been to the doctor. (You know which one: my doctor.)
Have you fed the dogs? (You know which ones I mean.)
Could you pass the salt? (You can see the salt that I want.)
- When we can't say 'You know which I mean', we:
- put a/an before a singular countable noun (see 65).
There's a rat in the kitchen!
I need an envelope.
- put no article with a plural or uncountable noun.
She's afraid of rats.
I need help.
In short, ask yourself "Does the reader know which I mean?",
- If YES, use the before that noun. (Have you fed the dogs?)
- If NO, ask yourself "Is it a singular countable noun?"
- If YES, use a/an before that noun. (I need an envelope.)
- If NO, use no article before that noun. (She's afraid of rats.)
Please note that these two basic rules, though cover most typical cases, are not complete. There are lots of exceptions and the real practices are so complex as StoneyB wrote.
Following the two basic rules, and knowing that training is uncountable and field is countable, it's now easier to see why the first "the summer training"(1) in your question is incorrect.
Company(name) has been providing the summer training(1) for engineers since 2010. We have been giving completely professional atmosphere for engineers to complete the summer training(2) with practical knowledge. Our each faculty has a great experience in the education field(3). We make sure you get all the important resources to make your summer training a learning and an enjoyable summer training. You may call or email us to get your confirmation about the training(4).
It's because you've never mentioned this summer training before, so the reader has no idea "which summer training" you mean. Writing "the summer training" in your first sentence will make it sound like your summer training is the "only" summer training in the world.
The other two "training"s: "the summer training"(2) and "the training"(4) are acceptable because "summer training" has already been mentioned in (1), so the reader now knows which "summer training" or "training" you are talking about. However, "this" might be a better choice, as StoneyB explained.
The part "the education field"(3) needs "the", because the word field is a countable noun, which means you need an article. To pick between "an education field" and "the education field", you might need to consider if "education fields" makes sense. (If you think you can say "an education field", you should also be able to imagine several "education fields".) And since "education fields" might not make much sense in your case, it's better to write "the education field".--Think of it like this: "It's a field. Which field? It's the education field."