time - Was man created before or after the animals?

According to Genesis chapter 1, it seems that the animals were created first. According to Genesis chapter 2, it seems that man was created first.

What are the different understandings that have been put forth to this question?

In Genesis chapter 1 we see:

Genesis 1:25:

כה וַיַּעַשׂ אֱלֹהִים אֶת-חַיַּת הָאָרֶץ לְמִינָהּ, וְאֶת-הַבְּהֵמָה לְמִינָהּ, וְאֵת כָּל-רֶמֶשׂ הָאֲדָמָה, לְמִינֵהוּ; וַיַּרְא אֱלֹהִים, כִּי-טוֹב. 25 And God made the beast of the earth after its kind, and the cattle after their kind, and every thing that creepeth upon the ground after its kind; and God saw that it was good.

Genesis 1:27:

כז וַיִּבְרָא אֱלֹהִים אֶת-הָאָדָם בְּצַלְמוֹ, בְּצֶלֶם אֱלֹהִים בָּרָא אֹתוֹ: זָכָר וּנְקֵבָה, בָּרָא אֹתָם. 27 And God created man in His own image, in the image of God created He him; male and female created He them.

In Genesis chapter 2 we see:

Genesis 2:7:

ז וַיִּיצֶר יְהוָה אֱלֹהִים אֶת-הָאָדָם, עָפָר מִן-הָאֲדָמָה, וַיִּפַּח בְּאַפָּיו, נִשְׁמַת חַיִּים; וַיְהִי הָאָדָם, לְנֶפֶשׁ חַיָּה. 7 Then the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

Genesis 2:18-19:

יח וַיֹּאמֶר יְהוָה אֱלֹהִים, לֹא-טוֹב הֱיוֹת הָאָדָם לְבַדּוֹ; אֶעֱשֶׂה-לּוֹ עֵזֶר, כְּנֶגְדּוֹ. 18 And the LORD God said: 'It is not good that the man should be alone; I will make him a help meet for him.' יט וַיִּצֶר יְהוָה אֱלֹהִים מִן-הָאֲדָמָה, כָּל-חַיַּת הַשָּׂדֶה וְאֵת כָּל-עוֹף הַשָּׁמַיִם, וַיָּבֵא אֶל-הָאָדָם, לִרְאוֹת מַה-יִּקְרָא-לוֹ; וְכֹל אֲשֶׁר יִקְרָא-לוֹ הָאָדָם נֶפֶשׁ חַיָּה, הוּא שְׁמוֹ. 19 And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto the man to see what he would call them; and whatsoever the man would call every living creature, that was to be the name thereof.

So according to Genesis chapter 1, animal is created before man, whereas according to Genesis chapter 2, man is created before the animals. Which is it?

One approach is to say that Chapters 1 and 2 are talking about the same events, but chapter 2 goes into more detail (as Rashi does). But if this is the case, there shouldn't be any contradictions between the order of events in each chapter.