The Participle is a non-finite form of the verb having some adjectival and adverbial characteristics.

These characteristics are manifested in its synthetic functions, - the main functions of the Participle are the attribute and the adverbial modifier.

Students reading English books in the original master the language easily.
Студенты, читающие английские книги в оригинале, легче овладевают языком.

Correcting your paper I found a lot of mistakes on the use of tenses.
Проверяя ваши бумаги, я нашел множество ошибок в использовании времен.

I've read all the books written by this author.
Я прочитал все книги, написанные этим автором.

Translated more skilfully this book could attract a greater number of readers.
Более точный перевод этой книги мог бы привлечь большее число читателей.
(an adverbial modifier of condition)

There are two Participles in English - Participle I and Participle II.

Participle I is formed by adding the suffix -ing to the stem of the verb and Participle II for regular verbs is formed by adding the suffix -ed and for irregular ones it is to be leant as the third from of the verb.

Note: Participle I of the verbs to lie, to die and to tie has the form lying, dying, tying.

Participle I has tense and voice distinctions and Participle II only has voice distinctions - it is usually passive in its meaning.

There were some articles translated from English in the journal.
В журнале было несколько статей, переведенных с английского.

Participle I has two tenses and two voices:

Active Passive
Indefinite writing being written
Perfect having written having been written

The tenses of Participle I are not absolute but relative, - Participle I Indefinite denote an action simultaneous with the action expressed by the finite form and Participle I Perfect denotes an action prior to it.

Reading this book I came across a lot of interesting expressions.
Читая эту книгу, я нашел множество интересных выражений.

Having written the program I decided to go to Greece for a holiday.
Написав программу, я решил поехать в Грецию на выходные.

There are some exceptions to this rule. With some verbs of sense perception and motion Participle I Indefinite is used even when priority is meant. These are the verbs: to see, to hear, to come, to come in, to look, to leave, to say, to look out, etc. The interval between the two actions is very short, they are almost simultaneous.

Hearing his voice she startled.
Услышав его голос, она заплакала.

Saying this the witch disappeared.
Говоря это, ведьма исчезла.