I am studying Present Perfect now and I am wondering if it is correct to say, for example:
The summer has been over
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Expanding on the correct answers in comments:
Summer has been over - This sounds rather incomplete although grammatical. Most native speakers would reserve this structure for use with a time frame. For example, Summer has been over for two weeks.
If you wish signal the end of summer, you have a few choices:
Present tense: Summer is over.
This gives a sense that summer has ended within recent memory. But, you can correctly say this in Winter, it is still a fact that Summer is over during the Winter.
Past tense: Summer was over or Summer ended.
This is perfectly acceptable as a stand alone. But, unless it is a bit of exposition setting the scene of a book, most would attach a time frame to this. Summer ended 4 weeks ago.
Present Perfect: Summer has ended.
This gives a sense that summer has just concluded recently. Compare this to the example you provided of Summer has been over which implies that it ended at some point in the past.
Past Perfect: Summer had been over.
Again, using the verb be here makes a native speaker listen for the completion of the sentence (usually with a time frame).
Continuous Present: Summer is ending
It's happening as we speak.
Continuous Past / Past Perfect Continuous: Summer was ending. Summer had been ending.
Summer was ending while something else was going on. Again, like the past tense, most uses for this would be in introducing exposition. (The PPCont sounds awkward.)
Perfect Present Continuous: Summer has been ending.
This is another that leaves a native speaker listening for the ending of the sentence. This has the limited use of a sentence like: Summer has been ending with higher temperatures every year.
The tl;dr version: Using the verb to end will be easier in most cases than to be + over.