Is the Gloria primarily a song of repentance, contrition and forgiveness or of praise? In the Gloria, we sing:


  Glory to God in the highest. And on earth peace to men of good will. We praise You. We bless You. We adore you. We glorify You. We give You thanks for Your great glory. O Lord God, heavenly King, God the Father almighty. O Lord Jesus Christ, the Only-begotten Son. 


This is evidently a praise chant. But then it follows:


  O Lord God, Lamb of God, Son of the Father: you Who take away the sins of the world, have mercy on us. You Who take away the sins of the world, receive our prayer. You Who sit at the right hand of the Father, have mercy on us. 


This feels more connected with the Kyrie eleison or related part of the penitential act, where we ask God for forgiveness. 

Then, the Gloria closes with:


  For you alone are holy. You alone are the Lord. You alone, O Jesus Christ, are most high. Together with the Holy Spirit in the glory of God the Father. Amen.


So, the Gloria still feels part of the penitential act and Kyrie eleison, sandwiched by praise to God. Is thus the Gloria more ritually (and perhaps spiritually) connected with the former, or is it supposed to be a break with the previous part of the liturgy?
The Institutio Generalis Missalis Romani is the document which instructs the pastors and the faithful on the correct way to celebrate the Eucharist. In its paragraph 53, it mentions the Gloria:


  The Gloria
  
  
  The Gloria is a very ancient and venerable hymn in which the Church, gathered together in the Holy Spirit, glorifies and entreats God the Father and the Lamb. The text of this hymn may not be replaced by any other text. The Gloria is intoned by the priest or, if appropriate, by a cantor or by the choir; but it is sung either by everyone together, or by the people alternately with the choir, or by the choir alone. If not sung, it is to be recited either by all together or by two parts of the congregation responding one to the other.
  
  It is sung or said on Sundays outside the Seasons of Advent and Lent, on solemnities and feasts, and at special celebrations of a more solemn character.
  


Therefore, the Sacred Congregation for Divine Worship and Discipline of the Sacraments, which edited this text, makes it explicit here that it is a hymn of glorification and entreating the Father and the Son. This identity as a hymn of primarily praise also explains why it is omitted in Advent and Lent, which are more penitential seasons. Finally, the "proper" name for the Gloria, Major Doxology, points to it being a hymn of saying (λογία logia) glory (δόξα doxa) to God.