Dose escalation part:to determine the highest dose of BYL719 administered on a daily basis when given in combination with weekly paclitaxel Dose escalation part: to confirm the safety and tolerability of the BYL719 and paclitaxel combination

Inclusion criteria For entire trial:

1. - Adult > or = 18 years old

2. - has signed the Informed Consent Form (ICF)

3. - has at least one measurable or non-measurable disease as per RECIST 1.1

4. - has tumor tissue available for the analysis as described in the protocol

5. - has adequate bone marrow and organ function as defined in the protocol

6. - is able to swallow and retain oral medication for the dose escalation part, ALL above PLUS

7. - has a histologically-confirmed, advanced unresectable solid tumors who have progressed on standard therapy (or not been able to tolerate) within three months before screening/baseline visit or for whom no standard anticancer therapy exists.

8. - has an Eastern Cooperative Oncology Group (ECOG) performance status ≤2 For dose expansion part, patient has ALL of above first six criteria PLUS either: 9- has a histologically/cytologically-confirmed HNSCC as detailed in the protocol and an ECOG performance status ≤ 1 or:

   • Patient is a Female with a histologically and/or cytologically confirmed diagnosis of breast cancer as detailed in the protocol and an ECOG performance status ≤ 1

Common exclusion criteria to Dose escalation and Dose expansion parts:

1. - has received previous treatment with a PI3K or AKT inhibitor as described in the protocol
2. - has a known hypersensitivity to paclitaxel or other products containing Cremophor
3. - has a contraindication to use the standard pre-treatment for paclitaxel
4. - has a primary central nervous system (CNS) tumor or CNS tumor involvement as detailed in the protocol
5. - has not recovered to grade 1 or better (except alopecia) from related side effects of any prior antineoplastic therapy
6. - has received radiotherapy > or = 4 weeks prior to starting study drugs, with exception of palliative radiotherapy, who has not recovered from side effects of such therapy to baseline or Grade ≤ 1 and/or from whom ≥ 30% of the bone marrow was irradiated
7. - has peripheral sensory neuropathy with functional impairment (CTC grade 2 neuropathy or higher)
8. - has undergone major surgery ≤ 4 weeks prior to starting study treatment or who has not recovered from side effects of such procedure
9. - has a clinically significant cardiac disease or impaired cardiac function as detailed in the protocol
10. - is currently receiving medication with a known risk of prolonging the QT interval or inducing Torsades de Pointes (TdP) and the treatment cannot either be discontinued or switched to a different medication prior to starting study drug treatment
11. - has diabetes mellitus requiring insulin treatment and/or with clinical signs
12. - has impaired gastrointestinal (GI) function or GI disease as described in the protocol
13. - has a known positive serology for human immunodeficiency virus (HIV), active Hepatitis B, and/or active Hepatitis C infection
14. - has any other condition that would, in the Investigator's judgment, preclude patient's participation in the clinical study due to safety concerns or compliance with clinical study procedures
15. - is currently receiving treatment with drugs known to be moderate or strong inhibitors or inducers of isoenzymes CYP3A or CYP2C8 as detailed in the protocol
16. - is currently receiving treatment with agents that are metabolized solely by CYP3A and/or have a narrow therapeutic window
17. - has a history of another malignancy within 2 years prior to starting study treatment, except cured basal cell carcinoma of the skin or excised carcinoma in situ of the cervix
18. - Patient has a history of non-compliance to medical regimen or inability to grant consent
19. - Pregnant or nursing (lactating) women
20. - does not apply highly effective contraception during the study and through the duration as defined in the protocol

For the HNSCC patient's cohort additional exclusion criteria are:

21- Treatment with more than one prior chemotherapy for recurrent/metastatic disease as detailed in the protocol 22- Prior taxane treatment for metastatic disease additional exclusion criteria for breast cancer patients' cohort:

- has received any prior cytotoxic therapy for the inoperable locally advanced (recurrent or progressive) or metastatic disease, or who had a progression/recurrent disease within 6 months after completion of an adjuvant/neoadjuvant therapy as described in the protocol

Other protocol-defined inclusion/exclusion criteria may apply