1 Timothy 2

1 I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men;

The meaning of the word “all” has often been misunderstood. In the Bible the usual meaning of the word “all” is “many” or “all sorts of man”. As it is in this chapter.
For example what would “all men” mean here? All men currently living? All men who currently live and who will be born? Or should we include the men who are dead as well? Is the meaning of “all men” really “all mankind”? From the context one could even make the argument that the phrase “all men” is explained in the next verse and that it would mean “kings and all that are in authority.” But I believe, and many before me, that the most faithful interpretation is “all kinds of men” or as John Owen has it “men of all sorts.”
The second reason for the world all is to contrast the current times with the previous times. In former times the Word of God was send to the Jews only. Now it is send to all, to the gentiles as well.
Readers interested in the meaning of texts like this and the meaning of “all”, “whole world” and texts like that should read The Death of Death in the Death of Christ by John Owen. Get the edition with an introduction by J.I. Packer as this contains a very useful outline of the work.

2 For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.

3 For this is good and acceptable in the sight of God our Saviour;

4 Who will have all men to be saved, and to come unto the knowledge of the truth.

"Who will have all men to be saved."
Does God want some to go to hell?

5 For there is one God, and one mediator between God and men, the man Christ Jesus;

"The man Christ Jesus"
Is Jesus God?

6 Who gave himself a ransom for all, to be testified in due time.

"Who gave himself a ransom for all."
Was Jesus a ransom for many or for all?

Given Matthew 20:8 it is best to interpret “all” here as meaning not only the Jews but the gentiles as well. To attribute the meaning “all of mankind” leads to the conclusion that although Jesus paid the ransom for some people, they will still be punished. And it is clear that not all will believe and therefore be saved, see Rev. 20:15. No, all those for whom Jesus paid the ransom, will be delivered. And this deliverance is freely available to all who believe in him, see Rev. 22:17.

7 Whereunto I am ordained a preacher, and an apostle, (I speak the truth in Christ, and lie not;) a teacher of the Gentiles in faith and verity.

8 I will therefore that men pray every where, lifting up holy hands, without wrath and doubting.

"I will therefore that men pray every where."
Should Christians pray in public?

9 In like manner also, that women adorn themselves in modest apparel, with shamefacedness and sobriety; not with broided hair, or gold, or pearls, or costly array;

"Women adorn themselves in modest apparel, with shamefacedness and sobriety; not with broided hair, or gold, or pearls, or costly array."
Women are to dress modestly, "with shamefacedness" -- "not with braided hair, or gold, or pearls, or costly array."

10 But (which becometh women professing godliness) with good works.

11 Let the woman learn in silence with all subjection.

(2:11-12) "Let the woman learn in silence with all subjection. But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence."
Can women be church leaders?
What the Bible says about women's rights

12 But I suffer not a woman to teach, nor to usurp authority over the man, but to be in silence.

13 For Adam was first formed, then Eve.

(2:13-15) "For Adam was first formed, then Eve. And Adam was not deceived, but the woman being deceived was in the transgression."
Men are superior to women since Adam was made before, and sinned after, Eve. But even though women are inferior to men, they shouldn't be discouraged because they shall "be saved in childbearing."
What must you do to be saved?

1 Timotheus

1 Timothy 2