Manifest Merger failed with multiple errors in Android Studio

So, I am a beginner into Android and Java. I just began learning. While I was experimenting with Intent today, I incurred an error.

Error:Execution failed for task ':app:processDebugManifest'.
> Manifest merger failed with multiple errors, see logs

I found some solutions here and tried to implement them, but it did not work.

This is my build.gradle :

apply plugin: 'com.android.application'

android {
compileSdkVersion 23
buildToolsVersion "23.0.0"

defaultConfig {
    applicationId "com.example.rohan.petadoptionthing"
    minSdkVersion 10
    targetSdkVersion 23
    versionCode 1
    versionName "1.0"
}
buildTypes {
    release {
        minifyEnabled false
        proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
    }
}
}

dependencies {
compile fileTree(dir: 'libs', include: ['*.jar'])
compile 'com.android.support:appcompat-v7:23.0.0'
}

This is my AndroidManifest :

<?xml version="1.0" encoding="utf-8"?>

package="com.example.rohan.petadoptionthing" >

<application

    android:allowBackup="true"
    android:icon="@mipmap/ic_launcher"
    android:label="@string/app_name"
    android:theme="@style/AppTheme" >
    <activity
        android:name=".MainActivity"
        android:label="@string/app_name" >
        <intent-filter>
            <action android:name="android.intent.action.MAIN" />

            <category android:name="android.intent.category.LAUNCHER" />
        </intent-filter>
    </activity>

    <activity android:name=".Second"
        />

    <activity android:name=".third"/>
    <activity android:name=".MainActivity"/>


</application>

This is my first week with coding, I am sorry if this is a really silly thing. I am really new to this and did not find any other place to ask. Sorry if I broke any rules

Open application manifest (AndroidManifest.xml) and click on Merged Manifest tab on bottom of your edit pane. Check the image below:

From image you can see Error in the right column, try to solve the error. It may help some one with the same problem. Read more here.

Also, once you found the error and if you get that error from external library that you are using, You have to let compiler to ignore the attribute from the external library.
//add this attribute in application tag in the manifest

   tools:replace="android:allowBackup" 
                                                                                                                                          
   //Add this in the manifest tag at the top

   xmlns:tools="http://schemas.android.com/tools"