Grammar
1. Да constructions
If you want to use a verb with another verb you have to put да between both verbs. But you have to be careful because the both verbs have to be conjugated:
Искам (I want)
Искаш (you want)
Иска (he want)
Ям (I eat)
Ядеш (you eat)
Яде (he eats)
So: I want to eat = искам + да + ям
You want to eat = искаш + да + ядеш
He wants to eat = той иска + да + яде
...
But if you want someone else to do the act:
I want you to eat – искам (ти) да ядеш.
I want you to go there – Искам (ти) да отидеш там.
See! The both verbs are conjugated in different way. The doer of the first act is „аз” (and that’s why искам). But the doer of the second act is “ти” (and that’s why ядеш, отидеш).
Here are you more examples:
Отивам да ловувам. – I go hunting.
Обичам да слушам музика. – I love listening to music.
Мразите ли да четете? – Do you hate reading?
Той иска да се прибират вкъщи. – He wants they to go home. … etc…
2. The impersonal verbs “има” and “няма”
Има = there is, there are – both singular and plural
Няма = there is not, there are not – both singular and plural
Има дете в парка. – There is a child in the park.
Има деца в парка. – There are (some) children in the park.
Има ли захар в чая? – Is there any sugar in the tea?
Има много книги. – There are lots of books.
Няма човек на улицата. – There is no person on the street.
Няма ли нови книги? – Are not there any new books?
But be careful!!!
Има means “he, she, it have” too
Няма means “he, she, it doesn’t have” too
Той има много книги. – He has lots of books.
Той няма пари. – He hasn’t got any money.
3. Aspect of the verbs.
Ok, boys and girls... Here comes one of the most difficult part of every Slavic language – the aspects of the verbs. If somebody of you learns other Slavic language(s) probably (s)he knows what I’m talking about.
The aspect of the verb is a way of looking at the action. There are two aspects of the verb in Bulgarian (and in the other Slavic languages) - imperfective (несвършен вид) and perfective (свършен вид).
The main difference between the imperfective and the perfective aspects in Bulgarian is that the perfective aspect implies a completed single action, while the imperfective aspect simply does not give any implication whether the action is single or not, whether it is completed or not. Very often, though, when opposed to the perfective aspect, the imperfective forms imply the opposite of what the perfective forms imply - a single but uncompleted action (i.e. action in progress) or an action that has been successfully completed more than once (i.e. iterative, habitual action).
Here are some examples:
Утре ще чета книга. – Tomorrow I’ll read a book.
Утре ще прочета книгата. Tomorrow I’ll read the (whole) book.
Утре ще дочета книгата. – Tomorrow I’ll read the book till its end.
Ще ти пиша всеки ден. – I’ll write to you every day. (that will be an usual act it the future and that’s why the perfect aspect of the verb is used.)
Ще ти напиша писмо. –I’ll write you a letter. (That will happen again – so the imperfect aspect is used.)
Мога да разказвам тази история много пъти. – I can tell this story many times. (”много пъти” (many times) – that means that will be an usual act in the future)
Искам да разкажа тази история. – I want to tell this story. (the act will be done only one time).
How to form verbs from perfect into imperfect aspect?
1. With the aid of prefixes:
Кажа – разкажа; питам – попитам, бера – събера, уча – науча,
2. with the aid of suffixes which might change the conjugation type of the verb:
Превръщам (3) – превърна (1), намирам (3) – намеря (2) , взимам (3) – взема (2), разказвам (3) – разкажа (1)...
Usually the verbs from the third conjugation type are in inperfect aspect as you see.
It is from a great use when you learn a new verb to learn its perfect or imperfect form because there is a difference when you say:
Превръщам се в котка. – I’m becoming a cat.
Ще се превърна в котка. – I’ll become a cat.
Ще се превръщам в котка. – I’ll become a cat. (but that means that you’ll become a cat many times, not only once.)
Превръщах се в котка. – I became a cat. (for many times but now I’m a human again)
Превърнах се в котка. – I became a cat. (and I am still a cat)
!!! The perfect aspect of the verbs usually can not be used in present tense. !!!
There are lots of verbs that have similar forms for the both aspects: имам (to have), арестувам (to arrest), женя се (to get married), отричам (to deny), управлявам (to govern, to rule over) and many others…
Okay...
have a look here
Anything unclear
Another perplexing thing is the presence of articles 
Hmm… and I suspect there will be more surprises ahead (like the Perfect tenses and so on). So the language looks really intriguing and I’d like to get to know it as better as possible. I’ve already studied the first 7 lessons and am waiting impatiently for the next one 
Knowing Bulgarian you'll be able to understand Macedonian as well. It is based on the Western dialects of Bulgarian.
Though I still don't know if it is a less complicated language than for example Croatian just because there are no cases. Any comments?