Hello, last time we were talking about how different aspect verbs can be used in complex and compound sentences, and today we will be discussing some special cases of their usage, as I promissed you before. So, let's start! :)
1) The first interesting question is how to use the verbs "мочь" (which is imperfective) and "смочь" (which is perfective). They are often mixed up with each other in the Past Tense and the Future Tense, where the forms of both exist. That's because both can be in principle translated to English with one and the same word or construction ('could' in the past, 'will be able' in the future). However, the forms of "смочь" are rather equivalents to English 'managed/will manage to'. So, when talking about someone's general capability to do something, we normally use the verb "мочь". To highlight that this or that action was/will be really taken, we're likely to use "смочь". The verbs "уметь" (imperfective) and "суметь" (perfective) are quite similar to ones we have just discussed.
2) When talking about the past, we can use both perfective and imperfective aspect verbs with negative particle "не", but the meaning of the whole (negative) sentence will be slightly different in these two cases. We use "не" + an imperfective aspect verb just to state someone didn't do something. When we use a perfective aspect verb instead of the imperfective one, we imply that they wanted to (or was about to) do something, but in the end did not do that. Just compare: "Сегодня Аня не ходила в университет" - "Сегодня Аня заболела и не пошла в университет", "Аня собиралась/хотела пойти сегодня в университет, но не пошла".
3) Have you noticed that after "не нужно", "не надо" only imperfective verbs can be used? On the contrary, after "нельзя" you can find either imperfective or perfective one, but there is a difference alright. An imperfective aspect verb after "нельзя" normally means something is not allowed (to someone in particular or to everybody): "Вам нельзя пить спиртное, пока вы принимаете это лекарство", "Здесь нельзя купаться". The combination of "нельзя" and a perfective verb usually states something is impossible: "Эту сумку нельзя поднять. Она слишком тяжелая!"
4) Finally, let's talk about the imperative. Imperatives are often used in Russian, actually, much more often than in English. We use them not only in requests and orders, but also to ask politely, to warn, to invite etc. How to tell one case from another? The verb aspect is the key point here. In short, in requests and orders (or when giving advice) imperative forms of perfective aspect verbs are normally used (in positive statements) and those of imperfective aspect verbs (in negative statements). Imperative forms of perfective aspect verbs in negative statements may be used to warn someone: "(Смотри) не забудь, мы выезжаем в восемь", "Смотри не упади, сегодня гололёд". Imperfective aspect verbs (we're still talking about imperatives :)) in positive statements may mean different things, but one of the most important cases is an invitation: "заходи (ко мне) на выходных - посмотрим мою коллекцию старинных книг", "угощайтесь", "проходи, не стесняйся".
Here are the main things to keep in mind. If you still have any questions, please do not hesitate to contact me!