The history of Chalukyas is a bit complicated with controversies and ambiguities ; and often riddled with myths and legends. Complicated, because there were many dynasties ( to be specific three ) shared the name Chalukya.
Before going further into this, let's first see where was this Chalukya Empire, as it is often referred, existed in India. Those of you with an understanding of the India's geography , imagine the Indian heartland bordered by two rivers - Narmada in the north and Kaveri in the south. Well, what lies between these two rivers was practically the span of Chalukyan Empire at its peak.
For the less acquainted in geography, the present day Karnataka, Maharastra , western districts of Andhra Pradesh roughly formed the Chalukyan Empire.
Leaving geographical part behind we'll see the three dynasties of Chalukyas and their relations. The so called 'original' Chalukyas were the oldest and had their capital at Vatapi (present day Badami near Pattadakal ) in Karnataka. So for the sake of clarity historians called them 'Chalukyas of Badami' or 'Early Chalukyas'.
Though the entire Chalukyan era spanned over 6 centuries (from 6th to 12th CE), the Chalukyas of Badami were prominent for about 200 years from 543 to 753 CE, till when the last Badami Chalukya king Kirtivarman II was overwhelmed by the ever expanding Rashtrakuta Empire.
The traces of Chalukya dynasty's split into two dynasties probably during the peak of its power. Pulakesin II, the famous Chalukya king credited for the expansion of the kingdom towards east. After the conquest of Vengi in 624 CE Pulakesin II appointed his brother Kubja Vishnu Vardhana as the Viceroy of the now conquered eastern part of the Deccan (parts of the present day Andhra Pradesh).
After Pulakesin II, the Vengi Viceroyalty developed into an independent kingdom. So this probably marked a new branch of the Chalukyan dynasty. Because this dynasty was based in Vengi and in the east of the Chalukya country , modern historians called them 'Chalukyas of Vengi' on simply 'Eastern Chalukyas'. Though smaller in its regional influence, this new found dynasy in the east outlived the parent dynasty - the Chalukyas of Badami - for may centuries.
So what happend to the 'original' Chalukyas, ie the Chalukyas of Badami? Badami was finally invaded by the Rashtrakutas in 753 CE. Practically that was the end of the Badami Chalukyas as a powerful dynasty.
Though their capital was conquered , the dynasty never came to an end. It survived as subordinate rulers under the shadow of the now powerful Rashtrakuta Empire. For another 200 years or so this status continued. Now came the time for the Rashtrakutas to succumb circumstances that led to its disintegration into many smaller kingdoms.
Tailapa II, descendent of the Badami Chalukya dynasty and a feudatory under the Rashtrakutas consolidated power of the region. This often marked as the revival of the Chalukya dynasty. They ruled most of the traditional Chalukya homeland from a place called Kalyana or Kalyani (present day Basavakalyan) in Bidar district of Karnataka. So again for the sake of better understanding the historians called this revived Chalukyas as Chalukyas of Kalyani' or more literally the 'Later Chalukyas'.
So that's a quick outline of Chalukya history. Most of the monuments you would see at Pattadakal was made during the Early Chalukya period. The architecture with bold expressions came to be called as Early Chalukya style. That is, the monuments built between the 6th and 8th century CE in this region of the erstwhile Chlalukya empire.
The Later Chalukyas too evolved a style of their own, often referred as the Kalyana Chalukya style , noted for its ornate carvings. You may not find this style in Pattadakal. The nearest site could be Lakkundi located close to Gadag, where the first versions of the Kalyana Chalukyan style was tried out. Mahadeva Temple at Itagi ( Koppal ) is a fine spaceman of the matured version of Kalyana Chalukyan style.
Chalukya Express connects Mumbai with Bangalore. That is Chalukya Express operates between Yesvantpur Junction in Bangalore and Dadar in Mumbai.The train is named so because its route passes is right through the erstwhile Chalukya Empire heartland.
Dedicated after Shiva, Kadasiddheswara Temple is the first temple you will be visiting as you enter the Pattadakal site. In size this temple is much smaller than say the Virupaksha Temple or the Mallikarjuna Temple , located further deep in the site. Possibly this temple was constructed during the regime of the Chalukya king Vijayaditya (696 - 733 CE). And this temple remains as an example of one of the earliest experiments the Chalukya clans did in the temple architecture. Otherwise this is built in what is called the Nagara style of architecture.