Two intermittent BD dosing schedules of AZD2014 in combination with paclitaxel will be evaluated. The 3 days on 4 days off schedule will examine 3 continuous days of AZD2014 per week in combination with weekly paclitaxel. The 2 days on 5 days off schedule will examine 2 sequential days of AZD2014 dosing in combination with weekly paclitaxel. For both schedules, a dose escalation 3+3 design will be used to establish the MTD and the recommended Phase II dose. Approximately 15 patients with solid tumours will be entered into each schedule during the dose escalation of this phase.