You should use "into" when it's a question of location, for lack of a better word. "I went into the store," "We went into the field of computer science," "We drank well into the morning," etc..
"In to" just happens sometimes. "I went in to buy some milk." In that sentence the "to" is part of the infinitive "to buy."
If you aren't sure which one to use, change the "in" to "in order" and see if it still works. "I went in order to the store" is wrong, but "I went in order to buy some milk" is good.
- I am studying PhD at the university.
- I am studying PhD in the university.
In the above, both sentences are wrong. Inserting for a between studying and PhD would make sentence 1. correct. Sentence 2. would still be wrong, as in is the wrong preposition to use in this case:
- I am studying for a PhD at the university. [Correct]
- I am studying for a PhD in the university. [Wrong]
This is not to say that the construction in the university is inherently wrong. There are certainly some contexts where this would be the correct form to use. For instance:
- The monument is in the university.
- He is in the university.
It is not always easy to come up with a rule to determine the choice between at and in. Some cases are clear cut, as in my first round of examples below. Others are not always so, as in my second batch of examples, for speakers tend to leave a lot of things implied in speech and in writing. Hopefully, you will be able to infer these rules from my examples.
In academic contexts, use at when referring to the institution in general or to a specific one. Note, however, that one would use in for graduate school or college (largely American context). The construction in university is also correct (largely British):
- I am studying for a PhD at the university.
- I'm at Oxford for a PhD.
- I'm studying for a PhD in graduate school.
- I'm currently in grad school for a PhD.
- I'm a sophomore in college.
- I'm in university for a PhD.
- I am studying for a PhD at Harvard.
- I am studying for a PhD at the Indian Institute of Technology in Delhi.
- I'm a PhD student at ETH, Zurich.
- I'm at King's College, London.
- I'm a junior at Williams College.
I should point out that in college and in university are rather colloquial constructions, but that's why they're used in everyday situations! In more formal contexts, it would be better to use at college/ at university.
More examples using school, department and faculty both explicitly and implicitly. Generally, in is used for department, while at is used for faculty:
- I'm studying for a PhD in the physics department.
- I'm in physics at MIT.
- He's a professor in the Department of Biology at Harvard.
- Are you the only assistant professor in this department?
- I'm a PhD student at the Faculty of Social Sciences in the University of Copenhagen.
- She's a professor at the Faculty of Arts and Sciences.
- My son is a lecturer in criminology at the Faculty of Law.
- I'm a PhD student at the Cape Town University Faculty of Law.
- I am in the School of Engineering for a PhD.
- He's a professor in Biological Sciences at Cambridge.
- I am a PhD student at the Yale School of Architecture.
- I'm studying for a PhD in the law school at Harvard.
- I'm a PhD student at Harvard Law [School].
NB: I did not look up information from any grammar book. These are just examples I came up with based on my experiences as a native speaker, general observations of usage, and what sounds right!
Best Answer
"lectures delivered in the University of Cambridge": Here we are talking about the location. Where were the lectures delivered? Answer: In the University of Cambridge. Here we know that the venue for these lectures was the University of Cambridge.
"lectures delivered at the University of Cambridge": Here the focus is on the institution. These lectures might or might not have been delivered in the university campus. But they were facilitated by the institution (University of Cambridge) as maybe a part of their curriculum or special lecture series or some other similar program.